A passkey is a FIDO2 “key”.
Could it be, that you’re using the inline autofill menu, choosing the passkey? – Because then exactly what you describe happens: you get logged in to Google, without clicking extra on the passkey in the “Bitwarden-passkey-popup”. – So, does it look similar to this:
?
(in my screenshot, you can see two passkeys, I get offered via the inline autofill menu…)