Forward university email to your protonmail account
PC and phone are not separated stuff, they are basically just different screen sizes. If you need some separation just make multiple protonmail accounts.
If you don’t feel like going through the pain of degoogling, yes, you would keep a gmail account just for basic android funtionality. that does NOT mean every app registration ever. Those are separated companies that allow you to register with google and you should not do that, register using email -> protonmail.