Including Firefox.
In 2019, Microsoft released an updated version of Skype for browsers. At the time of release, it only worked in Edge, Chrome and Opera, while Safari and Firefox were left out. A year later, the service still started working in Safari, and now Microsoft has confirmed support for all current browsers, including Firefox.
The mention of this was found in the description of the Skype 8.78 update. Already now you can go to web.skype.com through Firefox – and although there is a warning that some functions may not be available in this browser, you can use the service.
Probably, the warning will be removed with the release of Skype 8.78, which is now is in beta testing. Until then, the browser-based Skype may not work perfectly – but it's at least something.