In order to help anyone else on the internets passing by with this exact problem, allow me to explain how I eventually solved it.
0) Exit PNGTuber Plus
1) No idea if this is actually helping or not (possibly not) but I did swap over from PulseAudio to PipeWire. Considering PipeWire just does all the same things PulseAudio does, it's likely not useful here but most people that use Linux say it's not a bad move to make if you can.
2) Delete ~/.config/pulse. This appears to be your Pulse Configuration Files
3) Delete your godot data file (the one that pops up when you hit Escape). My guess is that this resets PNGTuber Plus to a default state, where it's then able to re-establish connection with your input drivers.
4) Type into the terminal 'systemctl --user daemon-reload' then hit enter. This just restarts your Audio Software because why not?
5) Then restart PNGTuber Plus. With a little fussing, it should work.
It's still not comfortable with switching audio devices too much and seems like this might be caused by trying to flick through devices too quickly and the system can't keep up fast enough. Once you switch to another device, it just crashes for good and refuses to work properly because now the settings data is likely writing nonsense. That's my absolutely guess here based on what I did to get it going again. I'm very much in the dark and simply want this program to work as well on Linux as it does on Windows.