I'm going to guess that the Site Access control is something in those 2 browsers, not the
extension (any extension, not just VDH). Mozilla just hasn't implemented such a feature
in Firefox. But if both Chrome & Edge have such a thing, it wouldn't surprise me if some
day Firefox acquired such a feature.
And I remember that thread, too. Was it this one?
https://groups.google.com/g/video-downloadhelper-q-and-a/c/h_fOnsQDjFc
It wasn't hundreds of tabs but it was a large number.