I'm really excited to see more and more people talk about FIDO2. If you're interested about this topic, I gave a talk about it yesterday: https://news.ycombinator.com/item?id=23689606
Here's a browser compatibility matrix (I know, OP is about SSH). FIDO2/U2F Just Works in: Chrome on Windows Firefox on Windows Chrome on Mac Firefox on Mac Chrome in Ubuntu 20 Firefox in Ubuntu 20 Wall of shame (FIDO2/U2F does not Just Work in): Safari EDIT: it does work out-of-the-box in Ubuntu 20, my bad.
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.