Sound is directed to HDMI irrespective of the selection of the (default) sink

I am new user here, posting after everything (google, ask friend, try around without actually understanding, what is happening) failed. The machine is:

https://linux-hardware.org/?probe=93002e901f

I am using only these two audio sinks, for media consumption:

$ pactl list short sinks
1   alsa_output.pci-0000_00_1f.3.hdmi-stereo    module-alsa-card.c  s16le 2ch 44100Hz   SUSPENDED
2   alsa_output.usb-EPOS_EPOS_BTD_800_A000871203803238-00.iec958-stereo module-alsa-card.c  s16le 2ch 48000Hz   SUSPENDED

and also have "Sound switcher Indicator" 2.3.9 installed, which just works fine.

Now, the issue:

1. When starting a media playback, it always starts via HDMI, irrespective of the selection of the (default) sink via pavucontrol/SS Indicator.
2. Further, listening to media via headset, in case of any media control input, like play/pause, next video, skip video, the audio playback immediately jumps to HDMI. Although SS indicator still displays headset as active, and in order to adjust the volume of HDMI, I have to manually select HDMI sink as active before, otherwise the system sound control will adjust the sound of the active headset, despite the fact that playback is directed to HDMI.

This happens e.g. on firefox when playing youtube. mpv with a local media file or a yt link is affected by the first problem only. the second problem is not present. vlc appears to behave like mpv, but in addition absolutely crashes the system (reboot required)

The problem is certainly made by me, because in the previous version of Ubuntu I was struggling to make the HDMI default sink. It appears I succeeded, but in a way I did not intended... :( Then, after some time I realized the problem and therefore, when updating the system to current 22.04.1 LTS version I chose to replace all "custom" config files to default ones. A further issue is that I can not recall changes made, as I made no documentation...

Now, since an update did not help, the only way to find a solution could theoretically be "rm -rf /" and then fresh reinstall. But I would like to avoid it... :)

Thanks in advance