What heirarchical deterministic derivation path is used for FIDO authentication on a Ledger Nano S? Does it ask for a different key each time or is it always the same key?

If I connect to Google for 2FA can it ask for proof of whatever key path they desire or does it have to be a particular key?

I'm wondering how much privacy I lose if I use a Ledger Nano S that is not exclusively for a particular accounts 2FA. E.g. What happens if I use it for multiple Google accounts, other companies, or have crypto currency. Could Google discover a Bitcoin balance if the same Ledger is used for 2FA?