Most solutions I've seen to this require some kind of external daemon to be running that takes care of launching ytdl for you (since most web browsers don't allow extensions to run arbitrary commands.)
Firefox _does_ have support for running this daemon-like-thing for you using Native messaging[0] though.
youtube-dl-firefox-addon[1] seems to employ this, so perhaps give that one a try?
I've been using a combination of firefox/chrome with youtube-dl/mpv+youtube-dl for a while
This comes very handy for playing high quality youtube videos on low end machines or downloading audio+/-video directly from youtube.
On the pre-webextension era of firefox/chrome , "open with" addon was the perfect fit.
Now, a special native messaging app needs to be installed to launch mpv/youtube-dl
"Open with" addon solved this by a python script (that obviously required installing python, and few other steps)
I decided to create a new tool to make this step easier and faster on windows: owclauncher[1]
Basically a lightweight native messaging host for "open with" addon: it is not running on the background, and only started (and immediatly terminated) by the browser when passing a command to any other program
You can check and compile the source code or the .bat windows installer/uninstaller
Firefox _does_ have support for running this daemon-like-thing for you using Native messaging[0] though.
youtube-dl-firefox-addon[1] seems to employ this, so perhaps give that one a try?
[0] https://developer.mozilla.org/en-US/docs/Mozilla/Add-ons/Web...
[1] https://github.com/akhilkedia/youtube-dl-firefox-addon