Technically, you’re not allowed to have multiple Google accounts from their perspective. So the tooling isn’t setup for it. You’re probably also looking like a bot to them.

I’d suggest using the profile feature in Firefox so you can configure different contexts based on your needs such as a personal, uni and spam profile.

They also sell a hardware authentication device that might help simplify matters. It’s called a Titan Security Key. You would need to research it to find out if it’ll support being bound to multiple accounts.