This is Firefox browser and it doesn't have control over facebook messenger any issues related to facebook accounts and apps should be directed to facebook support. And ask how to get video calls from facebook in Firefox working.

This happens when Facebook converts one of your chats to end-to-end encryption. They appear to be doing this one at a time and so you might be able to video some contacts but not others. I do not know whether it is Facebook's (Meta's) fault, and a serious lack of QA, or Firefox's (Mozilla's) fault.

I have looked for news of a fix but it doesn't even seem to be recognised as a genuine problem.

In my case, I an using facebook.com on a Windows laptop. Hence, I do not explicitly launch any Messenger App. I suspect your case will be similar.