EbiFri yes TOTP is possible, my accounts are secured via Aegis (Google wants to push you towards Google Authentificator, but you can usw any TOTP app).
In my experience once TOTP is set up, Google doesn't force a user to enter a phone number. I guess it's part of their security measurements and you are considered well enough secured with TOTP.
As for Aurora Store, I don't think it makes sense for your use case. It's mainly a Play Store alternative for people who don't use Play Services or don't want a Google account, but you'd still have to purchase your games through Play Store anyway... Also many games might not work without Google Play Services, and in app purchases won't likely work either. I recommend you stick to Sandboxed Play Services in a separate gaming user profile for what you want to achieve.