FastMail is still using the old FIDO U2F API; we’ve been planning on migrating to WebAuthn since it was finalised, but investigation revealed that the migration would not be entirely straightforward (especially if tokens registered with WebAuthn needed to still work with U2F, which at the time was important but could probably now be skipped), so we deferred it, since the U2F support is adequate for most users. I expect this is the experience with many small teams that support the FIDO U2F API. Documentation on migration is difficult to come by; I think
https://www.imperialviolet.org/2018/03/27/webauthn.html is the main source I’ve encountered.