Passkeys are just the product-facing name for WebAuthN, which FIDO2 devices should support. Theoretically, any FIDO2 device should support WebAuthN and therefore be used for websites, but right now there are a number of different implementations that each have their own quirks.
I am surprised that the FIDO2 key doesn't work on Google, but it probably just means that there is a bug somewhere in the implementation.