Short version: KDE puts the lovely buttons and sliders and stuff on the underlying audio system. What you’re seeing is done by ALSA/UCM, and wireplumber, not KDE. You might have more success asking about it elsewhere. But I’ll try to help.
Longer version:
Wireplumber should store your settings like mute, volume, default output, etc, and restore them on restart.
The files are stored in ~/.local/state/wireplumber/
There was a bug in wireplumber, a long time ago, which corrupted these files for some users. You may see success by simply stopping wireplumber (eg `systemctl --user stop --now wireplumber) and deleting them before restarting wireplumber. This is pure guesswork but it’s surprisingly common, and quick and easy to try. If you like you can move them, so that if it doesn’t work you can just move them back.
Check that wireplumber is stopped with sudo systemctl status wireplumber before removing them, or they will magically reappear exactly as they were.
After that you will need to set the sound system as you want it, and reboot the PC to see if that is remembered.
Prior to wireplumber seeing the devices at bootup, pipewire gets them. It will use UCM profiles and they can set volumes/mute states/etc on your card. Solving this is complex as you need to fix the UCM profile. Usually, wireplumber should override anything done there, anyway. (In theory. Sometimes not.)
Prior to pipewire seeing them, you may have a service running at boot. You can check them for example with sudo systemctl status alsa-restore.service and sudo systemctl status alsa-state.service
If you have something like that, and it has a broken state saved, you can overwrite it manually with sudo /usr/sbin/alsactl store. You probably want to make sure it’s correct in alsamixer prior to storing it.
Every time I’ve seen this problem of “it doesn’t remember my sound thing when I reboot” it’s been one or more of these three (and I had all three). The first and last are easy to fix, the middle one kinda sucks and I could help with identifying and working around that but it is best to report it upstream for a proper fix.
So try the first one and the last one and see how you go. Take backups before you change anything, just to be safe. Good luck!