Most likely not.

There had been a U2F API which later on had been superseded by WebAuthn (which internally uses the U2F protocol) and which is now shut down.

There is a good chance all your services are using WebAuthn.

I'm not sure but I think Firefox never supported the API which is now deprecated.

No. Webauthn is backwards compatible with old u2f tokens, so reguardless of how old your YubiKey is, it will continue to work.

Only site I use that uses U2F (and I enroll my keys everywhere I can) is Vanguard; every other site I use supports WebAuthn.