Maybe that's fine if all you want is to "lock" a sensitive page to people who aren't the device owner but that's pretty limited compared to FaceID to actually log in.
Almost all web sites should just implement WebAuthn. On a suitable iPhone or Mac users will be able to sign in by touching the sensor or looking at the camera, while on my Pixel phone I touch the fingerprint sensor, on this Linux desktop I touch a Yubico Security Key.
If your site is paranoid that some crazy user will choose a bad WebAuthn authenticator, or deliberately sabotage their own security for some reason, then you can use WebAuthn Attestation to obtain a signed document from the authenticator (yes, over the Web) which proves that it is, for example, an Apple iPhone 25 Super Mega Plus. I don't think you should bother doing that, but you can.
You just need an open standard, you could even embed the url of the validating api in the token, so anyone could create their own Face ID provider.