Same for me. Tried disabling personal data for all advertisers but you gotta go one by one, there's no Reject all option and there are way too many... so back to Connect.
The exact same for me, and I had just made a new account to use with sync for lemmy - logged in via sync, then read the privacy policy, logged out, and closed the app. I was crushed because now I couldn't even use the cool username I signed up with anywhere else either because now the admachines already knew it and probably already attached it to my device ID.
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.
I've been using DDG for tracking, and Connect had all sorts of weird tracking when I used it. Check it out with some network monitor and make sure it's not sending back your info.