Ok, in the past days I did a few things and documented what I did. I'm happy to let you know that I've found the source of my keyboard issue. Super long story very short: it was an USB extension cable
For everyone experiencing similar issues or interest in what I did, here is what I did
I installed TMK via my Ubuntu which is running on Win10
I took the code from Taran's Git and adjusted it for my F23 keymap (from here:
https://github.com/TaranVH/2nd-keyboard/blob/master/HASU_USB/NO_REPLUG_ISSUES_with_modifiers/keymap.c)
-> I attached my F22, F23 and F24 hex files in case anyone is interested in the modifier hex files that run with Taran's AHK script. I didn't test the F22 and F24 hex though, but they follow the same principle, see the *.c files.
I built my own hex files thanks to the documentation that Hasu was referring me to via TMK on Ubuntu - thanks for the tip, Hasu
(see:
https://github.com/tmk/tmk_keyboard/wiki#build-firmware)
I flashed my USB-converter using QMK Toolbox
Result: All keys, including the modifiers, could be used.
So I started testing. I re-started my PC, put it to sleep, woke it up, turned it off and turned it back on a few times to figure out two things:
1) The keyboard stays "online" as long as I don't turn off the PC. So I can re-start and put it to sleep without any issues. Once I turn it off, however, I have to replug the keyboard after turning it back on (see attachment with test results).
2) I do not have any of those nasty replug issues Zucca was describing i.e., I do not have to replug my keyboard multiple times until it works or anything like this described here:
https://geekhack.org/index.php?topic=69169.msg2738586#msg2738586. I only had to replug the keyboard once and then it worked again - always.
I then ran the same tests using Zucca's hex files (see
https://geekhack.org/index.php?topic=69169.msg2781175#msg2781175).
Result 1: All keys could be used, EXcluding the modifiers.
Resutl 2: The replug issue was exactly as described above i.e., only after turning off the PC the keyboard would go "offline" and only after repluging it once it would come "online" again.
I decided to read the entire communication between Hasu and Zucca to figure out whether I'm missing something.
There I found that you guys were talking about the energy savings options and that this was the root cause for the replug issues (see
https://geekhack.org/index.php?topic=69169.msg2740179#msg2740179).
I went to the Windows device manager and switched off all USB energy savings options I could find for the HID devices and also enabled that all USB devices could wake the PC from sleeping.
Result: No effect at all i.e., the keyboard would still need to be replugged after turning the PC off and on again.
Around that time I started questioning each single detail and recognised that the keyboard was plugged into the USB converter, and the USB converter was plugged into a 5m USB extension cable (a USB-female to USB-male cable, because my PC is "around the corner"), and my 5m USB extension cable was plugged into the PC.
So I ran a few tests without that 5m long USB extension cable by plugging in my keyboard directly to the PC. I switched it off and on and everything and then - it just worked - each time!
Then I recognized how stupid I was.
I remembered that my second keyboard never had the replug issue at all, however, the modifiers didn't work. When I decided to do something about the modifier issue, I changed the setup of my 2nd keyboard.
The whole time it was plugged into a USB hub. This USB hub was connected to the PC via a 5m long USB cable (no extension cable but rather a regular USB-male to USB-male 5m long cable)
My first keyboard, by the way, is using the same USB hub and experiences no replug issues ever, I recognized... but yeah, quite late... so yeah, quite stupid
However, my USB hub is in a very unhandy location for some (h)experiments so I decided using my 5m USB extension cable. And that was causing my replug problems when actually everything was performing correctly.
Once I bypassed the 5m USB extension cable but plugged the USB converter directly into the USB hub, I had no replug problems or whatsoever anymore. Plus, all modifiers are working now as desired <3
I'm happy now, thanks for your support Hasu
PS. I messaged Taran via Twitter, maybe he includes the correct hex files in his Git repository.