I do not think that this is Firefox specific, more likely is is something Linux specific.
For me, hCaptcha has stopped working immediately before last weekend, regardless of the site that uses it.
It goes in an infinite loop, despite solving correctly all challenges.
On Linux, I have tested with 2 browsers, Firefox and Vivaldi, and the browser did not make any difference. I do not use any ad blockers, nor any non-standard extension.
So I think that they deployed a version update last Friday, which for some reason is broken on Linux.
It would not be surprising if both hCaptcha and Google ReCAPCHA have made some similar changes, so now they are both broken on Linux.
Meanwhile, some other "Captcha" applications from other vendors, which are used on other sites, still work like before.