I currently have all of my 2FA codes in Pass except for my Proton account itself, which I have in Aegis, backing up to my home server.

It looks like you can easily export from Aegis to Proton Authenticator and you can use PA without a Proton account, which I think I might do. I don't want to use my PA app with my Proton account to hold my Proton account 2FA code. I'll end up locked out of the house with the keys inside.