GA collects very limited information by default. You have to go pretty far out of your way to give Google usernames, posts, etc for ad purposes. It's likely the only thing they received was a device identifier generated specifically for the new install of the app. You're fine.

You most likely can use the account, unless the author is intentionally doing something shady, Google doesn't know your username from this interaction.

Yeah that's the shitty thing about interacting with these corporate spying services, they're very good at invading your privacy and making connections to break your anonymity.