Do you have monitoring turned on or off for your tracks?
https://steinberg.help/cubase_pro_artist/v9/en/cubase_nuendo/topics/recording/recording_monitoring_via_cubase_t.html

Once again ... I ... can't ... hear ... anything!

And I am pretty pissed off btw.. Obviously everybody on this wide world simply puts a cabel in a hole and everything is running. WHY NOT ME???

It's hit and miss. In general, you see some who continually have problems and some that don't.

On my keyboard for most DAW recording modes the Main L/R outputs are silenced (local monitor turned off, on the keyboard side) and what's supposed to happen is audio is sent over USB to the DAW and then the DAW's job is to get that audio back, over USB, to the keyboard.

If Local Monitor is turned on - you should hear everything direct from the keyboard but it may mis-align with say plugins that are controlled by the keyboard (if you do any of that).

EDIT: not sure how I got off the tracks and initially responded with "YC". Turns out I can help more directly.

Under [UTILITY] "Settings" -> "Audio I/O" turn on (or make sure it's on) "Direct Monitor". This is a debug step. You should hear audio unless either the sound reinforcement isn't working (which I doubt) - or if local control is turned off which sends MIDI to the DAW expecting the DAW to echo back this MIDI data and your DAW's MIDI routing is the issue.

https://www.youtube.com/watch?v=ZPPJeU9Ayy4

If the problem is with MIDI routing then the above video is one way to setup MODX. MIDI tracks are added and each track has MODX as its output. I'm not sure this is covered, but MIDI thru (in Cubase) is turned on to make sure data coming into the DAW from MODX is echo'd back out to MODX on the corresponding track MIDI channel. This is what makes the tone generator sound. Without the MIDI routing setup - MIDI is only sent out the keyboard to the DAW and not to the tone generator so no sound will be heard.

If you wanted to test for this kind of problem, you would go into [UTILITY] "Settings" -> "Local Control" and turn this on. Ultimately it's not the best configuration - but at least now you do not need the DAW to echo anything back.

I really, really, really stressfully managed over weeks to craft a serious Cover-Song. All problems, all Yamaha insufficiencies ... I solved them. And now I can't get it out of the MODX. A simple audio recording ... that is really ridiculous.
Holy modern times ... buying Monitor boxes, putting a microphone infront of them and press "record"-button on the front of a tape-machine.

And one thing is clear: forget about those quick settings. They mean nothing. By the way it allways jumps on "standalone". The settings are still the chosen ones, but it allways shows "standalone".
You will have to study all the items behind those walls of science to get this running. Nothing is "quick" here. Nothing!

One examples of the thousand ways I tried it:
- I have the german version, hope the translation is near the original
- set the MODX on "audio record in DAW"
- starting Cubase
- choosing preset "Yamaha multi channel recording" ... because it is the (only) one, where "audio record" is mentioned
- "creating"
- popup-window ... choosing a folder
- no clue ... I don't care ... pressing enter
- "reading USB channels" says a new popup window
- and once again a new popup window, where all "assigned ports" are "not assigned"; USB Main L/R and USB 1-8.

I'm sorry to derail you here.... but I've been down this road... and found two offramps that led to greater success.

Cubasis (the old one) on an iPad, almost "out of the box" is good at audio recording the MODX.

or...

Reaper, on your PC or Mac. This is a lot more fiddle, you have to set each track carefully to get the most/best options, but having done that, you can save it as a template, and it works every next time... but... one trick.... ALWAYS plug your MODX into the exact same USB port.

This is important on a PC because they have a tendency to create differing configurations of USB-MIDI from each unique USB port. And important on a Mac because performance is different out of each USB port. Generally speaking, the ones on the left of a portable Mac are faster, and if there's two on that side, the one nearest the screen will be faster. Generally speaking. Not always the case.

And one thing is clear: forget about those quick settings. They mean nothing. By the way it allways jumps on "standalone". The settings are still the chosen ones, but it allways shows "standalone".

I've complained about this poor user experience choice. The box around "Standalone" doesn't mean anything. Every time you navigate back to the template selection screen, "Standalone" will appear with a box around it. If the last quick template you selected was "Audio Rec on DAW" then as long as you didn't change Performances or manually change the parameters that are altered by "Audio Rec on DAW" then all of the settings remain even though "Standalone" has a box around it.

Each of these buttons is a shortcut to setting various parameters in the [UTILITY] settings as well as some in individual Part parameters. These same settings can also be altered (not by pressing the template buttons) by:

1) Loading a backup or user file that contains different settings
2) Changing (recalling) Performances which will bring in that Performance's settings.
3) Manually changing the [UTILITY] settings or Part related settings.

If you press "Audio Rec on DAW" and do not load new backup/user files and also do not switch Performances and also do not alter settings that are changed by this quick template then those settings will remain no matter where the box is around Standalone.

I have feedback until I'm blue in the face (to Yamaha) about how poor of a choice this is. Because it implies something untrue and ultimately is unnecessarily confusing.

Although I tried asking some questions this didn't seem to pan out (I didn't get any answers).

Maybe read through this which explains some of the "why" I was asking about certain settings:

https://yamahasynth.com/learn/modx/part-1-mastering-modx-audio-record-on-daw

... it talks about the cubase monitor (speaker) button I asked you about. It talks about direct monitor (but doesn't say to turn it on if you have problems as I suggested you to try). It walks you through things step by step.

Documentation isn't infallible - but hopefully this will help get some traction.