Sorry to hear you lost all your data, but the details you’ve given don’t quite add up. Or we are not following them... below we have some questions, hopefully to clarify what actually happened.

If when you say you made a “successful” backup, if by this you made a BACKUP FILE (.X8A) using the MODX to a USB stick. if it was successful does that mean it was created and all is normal — or what do you mean “successful”. Why is that not the end of the story?
Maybe you mean something different. Successful to me means the data was created and you verified it...* (the MODX will show you the size of the Data File

If you used the MODX to make the Backup File, the data is not purged from your instrument... all the data in that Backup File is still resident in your MODX. The act of making a Backup File does not delete any data. You say you wanted to load this Backup File - ?WHY? - isn’t the data already loaded? Why did you need to load it? Or did you leave something out.

133KB — ? Is that the size of your successful backup?

Just FYI, the MODX is (normally) incapable of creating a Backup File that small ...unless the instrument was INITIALIZED prior to making the file.
As I recall a completely empty MODX will have 132KB of data right after you execute “Initialize All Data”
An empty MODX file has nothing for the Melas Waveform Editor to load.

Completely empty means no Songs, no Patterns, no User Performances, no User Arps, no Libraries, no Live Sets, no Motion Seqs, and no Waveforms.

Other curious statement: “Since I didn’t give it a new Backup name, I deleted the old one from Contant because I didn’t want to overwrite it.”
Just what does this mean exactly? How did you “delete” it? You should always give your File a New Name. Always! By giving the file a New Name this avoids it Overwriting anything. Only if the Name is exactly the same (on the same storage device) will it offer to “Overwrite?”

About your Songs and Patterns
Songs and Patterns will remain in the MODX’s internal memory until you either:
__ Manually DELETE them
__ You initialize your MODX using “Initialize All Data”
__ You load a .X8A File (Backup File) which will contain other Songs and Patterns

In other words, simply loading a USER File (.X8U) or a LIBRARY File (.X8L) will not disturb your Song and Patterns data.
Press [UTILITY] > “Contents” > “Data Utility” > the folders marked “Patterns” and “Songs” will contain the Patterns and Songs (up to 128 each) that you’ve either created using the MODX, or that you have loaded.

Check your Folders. Let us know...

This file was MODXBackup 2. I created a total of 5 Backup files.

MODXBackup 1 (Best of)
MODXBackup 2 (Dance and Trance Voice library)
MODXBackup 3 (EasySounds voices)
MODXBackup 4 (Analog Synth Voices)
MODXBackup 5 (Jean Michel Jarre voices)
I have always used the appropriate Backup for the current production. More backups because 1g of FLASH doesn't fit everything.
The MODXBackup 2 had two songs and the associated Performance settings. I made minor changes to the songs and wanted to do an improved MODXBackup 2. I didn't want to overwrite the old MODXBackup 2 because once the MODX crashed due to an overwrite and for some reason the file was corrupted, so I deleted the old MODXBackup and when I created a new Backup file for the patch, its name remained MODXBackup 2. No I gave him another name. The same problem as before was that after Intitalized All I wanted to load MODXBackup 2 the file loading stalled. Because MODX8 Backup could not be loaded file. ( I do not understand why?) Thus, 1gb of data became 133kb. I've been thinking about that because of the external HDD? It has worked well so far. The data was not on a pendrive, but on an external HDD. Is it possible that the external HDD is faulty and the file is damaged during loading? So the MODXBackup 2 file was created but the file was corrupted during loading. The file was OK before that. So I ask, is it possible that the MODXBackup 2 file is corrupted due to the external HDD?

You are plugging an external hard drive directly to MODX? If so, that would not be regarded as a supported configuration. The "USB TO DEVICE" port has a compatibility list of what should be plugged in to that port. The list has only USB Flash Sticks - not mechanical or SSD drives. The issue with anything but a USB (pen) flash drive is that these devices typically draw more power and even sometimes "cheat" drawing too much power. Beyond that - since these devices are not supported - Yamaha does not test compatibility with them.

Here's what the owner's manual states regarding the USB TO DEVICE port:

Precautions when using the [USB TO DEVICE] terminal
==============================================

This instrument features a built-in [USB TO DEVICE]
terminal. When connecting a USB device to the terminal, be
sure to handle the USB device with care. Follow the
important precautions below.

NOTE
For more information about the handling of USB devices, refer to the
owner's manual of the USB device.

Compatible USB devices
====================
• USB flash drive
Other USB devices such as a USB hub, computer keyboard
or mouse cannot be used.
The instrument does not necessarily support all
commercially available USB devices. Yamaha cannot
guarantee operation of USB devices that you purchase.
Before purchasing a USB device for use with this instrument,
please visit the following web page:
https://download.yamaha.com/
After accessing the Support website (and clicking on
“Documents and Data”), enter the appropriate model name.
Although USB devices 1.1 to 3.0 can be used on this
instrument, the amount of time for saving to or loading from
the USB device may differ depending on the type of data or
the status of the instrument.

NOTICE
The rating of the USB TO DEVICE terminal is a maximum of 5V/
500mA. Do not connect USB devices having a rating above this,
since this can cause damage to the instrument itself.

Connecting a USB device
====================
When connecting a USB device to the [USB TO DEVICE]
terminal, make sure that the connector on the device is
appropriate and that it is connected in the proper direction.

NOTICE
• Avoid connecting or disconnecting the USB device during
playback/recording and file management operations (such as
Save, Copy, Delete and Format), or when accessing the USB
device. Failure to observe this may result in “freezing” of the
operation of the instrument or corruption of the USB device
and the data.
• When connecting then disconnecting the USB device (and
vice versa), make sure to wait a few seconds between the two
operations.

Using USB flash drives
===================
By connecting the instrument to a USB flash drive, you can
save data you’ve created to the connected device, as well
as read data from the connected device.

Maximum number of USB flash drives that can be used
===========================================
Only one USB flash drive can be connected to the [USB TO
DEVICE] terminal.

Formatting USB flash drive
=====================
You should format the USB flash drive only with this
instrument (page 61). A USB flash drive formatted on
another device may not operate properly.

NOTICE
The format operation overwrites any previously existing data.
Make sure that the USB flash drive you are formatting does not
contain important data.
NOTE
For details on how to format the USB flash drive, see the Reference
Manual PDF document.

To protect your data (write-protect)
==========================
To prevent important data from being inadvertently erased,
apply the write-protect provided with each USB flash drive. If
you are saving data to the USB flash drive, make sure to
disable write-protect.

Turning off the instrument
====================
When turning off the instrument, make sure that the
instrument is NOT accessing the USB flash drive by
playback/recording or file management (such as during
Save, Copy, Delete and Format operations). Failure to do so
may corrupt the USB flash drive and the data.

Thanks for the reply Jason! This was a very useful help. I no longer use an External HDD, only a Pendrive. The error was then clearly due to the external HDD. Thanks for the quick reply everyone!

Regardless of all above, I suggest a BETTER PRACTICE for making backups.

TLDR - OPs practice of making backups is guaranteed to run into disaster. Your time and work is valuable. I suggest you read and follow this practice below.

In relation to the Disk Storage capacity on a PC or MAC - a 1Gb backup file is nothing, it is a drop of water in the Ocean.

You are employing an unnecessary "tidy house" policy by either overwriting your previous/older backup, or worse, deleting the Old Backup, BEFORE you make a New Backup.

Think of it like this. Every time you take new photographs of your family, do you erase all the old ones? I suspect not.

Backup Files are basically a fall-back safety net, which can be used to RECOVER from a disaster, without losing ALL the work you ever did. DISASTER can be a memory failure on your MODX, USB, PC HDD. It could be something as serious as a house fire.

Here is what I recommend.

You clearly move between 5 different configurations:-

MODXBackup 1 (Best of)
MODXBackup 2 (Dance and Trance Voice library)
MODXBackup 3 (EasySounds voices)
MODXBackup 4 (Analog Synth Voices)
MODXBackup 5 (Jean Michel Jarre voices)

There are too many letters for individual file names. You need to code it down, and assign accronyms you understand. For example:-

1 BEST
2 DTVL
3 ESVX
4 ALOG
5 JMJV

You need to have comprehensive DATE naming convention. I highly recommend using the following format:-

Today is 17th January 2021. The Date tag in your file name would be written (by you) as:-

20210117

26th Feb 2021
20210226

Your backup file name (TODAY) is then called, for example:-

DTVL20210117

or future back up, say 29th March 2021.

DTVL20210329

NB: THIS STORES THE ORIGINAL CREATION DATE IN THE FILE NAME. It prevents the original date being overwritten by a "last modified" date in the PC/MAC. Believe me, doing this will save you a lot of headaches down the road, if the files are ever copied or moved.

There is no need to write "backup" in the filename - that is indicated by the .file_extension i.e. .X8A

Store your backups immediately from the USB Flash to your PC/MAC. Backup up your PC regularly to the Cloud or an external/portable HDD.

If you create a folder on your PC called "YAMAHA MODX BUPS" and store all your backup files in there, the file names will be automatically listed in Name and Date order e.g.

BEST20210103
BEST20210110
BEST20210117
DTVL20210102
DTVL20210104
ESVX20210111
ALOG20210109
ALOG20210114
JMJV20210103
JMJV20210106

Now, whatever goes wrong, you have multiple step back, and rewind options to "start again". The most work you will ever lose is the work you did since your last backup. This may be a few hours, but better than losing 6 months!

Another advantage is falling back to an older version of your files, even if there was no disaster.

For example, in November 2020.... you had everything sounding just how you wanted. But come Jan 2021, you thought you could make some improvements. So through Jan, Feb, March you start tweaking everything, but by April, you have lost your way, and now everything sounds a lot worse than Nov 2020. You can't remember what you changed, why or where you changed it. You wish you could "rewind" to November 2020.....

Now you can, you just load up NOV2020 backup (but DO NOT ERASE all backups since NOV2020... you will regret doing this). You can re-evalute where you were in NOV2020 and compare to where you are in APRIL2021. This might be enough to see where problems where introduced, and fix them in APRIL2021 versions.

Hope this helps.