Songs, in MONTAGE, are any .mid Files that you have loaded from a USB drive or you have recorded directly to the MONTAGE onboard Recorder. You should have saved these separately to a USB stick as .mid files. They can be reloaded.

Songs (128) of them can be held in the [UTILITY] > “Contents” > “Data Utility” > “Song” Folder.
This Folder is saved and restored, all together, by the BACKUP FILE (.X7A) Type, only. The BACKUP File was added to the MONTAGE at version 1.50.x so you should have created a .X7A file prior to executing the firmware update... as outlined in the README file that accompanied the firmware Download. Restoring the .X7A File after the firmware update would restore all content in your MONTAGE (including your Song Folder) as it was before the firmware update.

If you did not create the BACKUP File, then you can restore your Songs by loading them, one by one, from your original source .mid Files. All .Mid files loaded will remain in the MONTAGE Song Folder until you Delete them, or you Initialize all data (which can happen when you update your firmware).

Hope that helps.

Extra Credit:
.mid Files that you loaded in from a file can simply be reloaded. But any recording you did directly to the Performance Recorder, that you did not opt to save as a .mid, will be lost. After recording to the internal recorder you are offered an option to save as a .mid File (highly recommended). Alternatively, you can use MONTAGE CONNECT to drag your Songs from the Song Folder to your computer via the USB cable. MONTAGE CONNECT, additionally can archive the Performance as a separate .X7B (Bulk) File.

MONTAGE CONNECT has a window labeled “Songs”... when the program in ONLINE, you view and access the current contents of the MONTAGE Song Folder. It is a good workflow to always additional back up your Songs by dragging them to your computer or dropping them into your favorite DAW. For example, you can have Cubase set so when you drop it in an empty Project, each Part goes to a separate MIDI Track assigned to the MONTAGE.

From the download page: https://usa.yamaha.com/support/updates/montage_os_updater.html

Caution
=========
MONTAGE Connect software is also updated. Please see "Related Downloads" below.
This updater is only for the MONTAGE synthesizer.
This updater is to be used at the user's own risk.
All User data (Libraries, User Performances, Song and so on) will be initialized by this updater. Please make sure that you have saved all User data to a USB flash drive before performing this update.
The unit may become inoperable if the electrical supply is interrupted while running the updater (by disconnecting the AC cord, etc.). If this happens, run the updater again from the first step.
If the unit does not function after running the updater, please contact your nearest Yamaha service center.

On the webpage - the following is in bold red text "All User data (Libraries, User Performances, Song and so on) will be initialized by this updater. Please make sure that you have saved all User data to a USB flash drive before performing this update."

Notice how the caution identifies that "All User ... Songs ... will be initialized by this updater".

What is unfortunate, within this page, is that there is no clear indication that your backup type should be an X7A (all) file. It instructs you to backup your user data - which may mislead one to think that a user file (X7U) is sufficient to backup all items on the list that will be initialized. A user file backs up:

Files of the “User File” type saved to USB flash memory
can be loaded and restored to the dedicated area in the
User Memory of the instrument (page 22).
User File Type data is as follows.
• Performance
• Arpeggio
•Motion Sequence
• Curve
• Live Set
•Micro Tuning
•Waveform
• Utility settings
• Quick Setup

An X7U does not back up song data.

I'd strongly advise Yamaha to revise the instructions for firmware updates located on the download page so that it is clear that only a full backup (X7A) will preserve the data that will possibly be erased by a firmware update.

... that said, if you look at the README inside the firmware update ZIP file, it states:

Updating Procedure

NOTICE:
All User memory (Library data, User data, User sample and so on) will be initialized by this updater.
Please make sure that you save all User data to a USB flash drive before performing this update.
With earlier versions, the Library data cannot be backed up. Please prepare the original library data.
In addition, when you load backup data, load libraries first before the user data.
With version 1.5 or later, make sure to use the backup file (.X7A). For details, refer to the Supplementary Manual.

If you were updating from a version earlier than 1.5 - then the instructions above are incomplete with respect to song data. However, if your previous firmware was 1.5 or above - then the instructions guide you to bake an X7A full backup.

Still - the update instructions should be as robust as possible in all locations. Both the readme and webpage could use some tweaks. The webpage adding details about full backup and the readme adding details about having to save off songs individually if your pre-update firmware does not provide a way to do full backups (earlier than v1.50).

Thanks guys. I recall seeing the instructions to use the BACKUP option. But I did not see that option when I did my backup. Perhaps I was on a version prior to 1.5? I was going by memory on that, so could be wrong.

If using something earlier than 1.5 you would have had to either save your songs to USB from Montage or use Montage Connect "Song Import". Song import from Montage Connect is probably the easiest pre-1.5 way to have accomplished this. Because it's a more-or-less 1-step operation. No poking USB sticks in and out of different devices.

If songs were ever part of what could have been initialized, it would have been "nice" (and it would still be nice - since not everyone is upgraded to >=v1.5) to have instructions to use Montage Connect to "Song Import" the songs to back them up.

I know it's water under the bridge for you - but still room for improvement to help guide others who may cross this point in the future.