New web sites should do WebAuthn to enable this functionality, here's a guide someone else wrote that I found helpful in talking about the moving parts to actually implement this: https://webauthn.guide/
Firefox's WebAuthn implementation isn't as complete as it would ideally be, but it does have a nice feature of asking the user whether to give out the somewhat privacy-infringing "attestation" from a FIDO2 device when it is requested by a web site. IMNSHO ordinary web sites, especially where a second factor isn't even mandatory, should not be asking for attestation and I always refuse.