Ah, crap. Sorry, I forgot about that part of your question. You’re right that Piezo would be too simple for your needs.
I’m actually thinking the best combo for you would be SoundSource ($39) plus BlackHole and QuickTime.
SoundSource can be used to send the audio of a single app to BlackHole and then you can set the microphone in QuickTime to BlackHole.
Unfortunately, there are very few options out there to do this sort of stuff reliably. Another option might be SoundDesk but I’m honestly not sure how well it would work. Plus, I don’t think they have a native Apple Silicon version available yet if that’s important to you.