I agree with Chris. YouTube support in QTE has always been messy and prone to glitches, and I suspect that something has changed in the API on the other end that it uses. The other possibility is they may be enforcing TLS 1.2, which TenFourFox supports but QuickTime doesn't, and QTE uses QT natively for network transport.
Chris pointed me to a downloading app, downvid that worked OK but suddenly
it has stopped working and instead of downloading a selected mp4 it gives
me a page of random other videos. I installed the new release of TFF and
now there is no more navigation bar on the YT page. Can't watch any YT
videos anymore. Not an improvement. Thanks anyway.
Youtube keeps changing its backend and the download sites must keep up, some are better at it than others.
Youtube also has changed their frontend layout a bit; I now get two navigation bars (one on top, one to the left) but this may vary with screen size, maybe also by country. It certainly has nothing to do with the TFF update.