With that done, GitHub prompts me for my key. My Linux office workstation is missing the necessary udev rule, so I couldn't test more. (Funnily, pressing Cancel caused them to send me a SMS, so their 2FA is practically worthless).
I've run into strange interactions where adding a key is disabled in Firefox (even with the security.webauth.u2f flag set to true), but once one key is added, you can add subsequent keys no problem.
This is how Github worked for me - I think it's just a mis-match in the code checking for U2F functionality...
I think adding the key use a different mechanism - there are two JS interfaces for U2F, and FF only supports one of them.
TBH I've added my key to GitHub with chromium, but have since moved to FF; so that might be what you're seeing with GitHub.
With that done, GitHub prompts me for my key. My Linux office workstation is missing the necessary udev rule, so I couldn't test more. (Funnily, pressing Cancel caused them to send me a SMS, so their 2FA is practically worthless).