Thank you so much for the care and attention you took while writing your reply. Though, whatever I did, I could not make this website NOT translate it into my native language in a choppy way. If there is a way for me to be able to read your replies in their original English, please tell me.
But back to the sound issue. About the chart you provided, that isn't really how it is. My computer used to be able to project sound onto my Philips monitor, but now it does not recognize it as an output; no matter if there are external speakers attached onto the monitor (my wish is to be able to connect the speakers to the monitor so that I could use them [the monitor and speakers] with other devices too, such as my XBOX). I really can't pinpoint a time when this issue began, I think it was when I was experimenting with connecting the speakers to the monitor. Well, on the other hand, my XBOX, which I have also connected to the monitor, has no issue with sounds.
Solutions I have tried:
- Trying a different HDMI cable
- Messing with a lot of options on the sound manager and device manager, such as uninstalling and reinstalling relevant devices
- Using third party applications to try and fill possible up-to-dateness gaps in my drivers (though I had problems providing better drivers for the AMD graphics card. I know that the HDMI is connected to that, but is that even relevant?) (also, a driver I installed changed some sound stuff of AMD to Realtek; is that even compatible? more info on the screenshots)
- Messing with all the audio options on the monitor (then setting them back to default because they did not work)
- And more that I can't remember
Screenshots:

Hoparlör (Voice.ai) is irrelevant
Hoparlör (Realtek High Definition Audio) is the sound system. It works fine when diriectly connected to the PC, but I want it to work through the monitor (with surround mode).
I **** not sure what Realtek Digital Output is. It had a different name before I tried some third party driver apps, something like S/PIDF. It has not given off any sound and I **** not sure if it is supposed to be the monitor, or relevant to it.

The devices from the device manager that I think might be relevant to the issue. I have tried updating them and stuff. They're in Turkish, sorry for the inconvenience.

The mysterious HDMI outputs that I can't remove nor use. Is one of them supposed to be the monitor? The monitor is obviously connected to the computer right now, then why does it not show any of them to be connected?
These are the rest of the outputs.
I have tried the secure mode solution you have offered, but I could not really understand what to do in it (maybe because your reply is translated to choppy Turkish). There the Windows just did not see any of the sound outputs at all.
This is all the information I figured might help you in helping me. Don't hesitate to ask for more if I forgot to provide anything important. Thanks for the service!