Linux

If you want vertical tabs with the ability to organize them in trees I suggest the Sideberry extension. It legitimately makes me nervous that the functionality would ever go away, it improves my productivity so much.

You can bookmark trees, collapse them, search them, load/unload them manually, I could go on. It makes it easy to organize dozens or hundreds of tabs. I have some trees for emails, news, forums, projects, etc. When I'm done just fold it up: the top tab bar can hide tabs that aren't in the active tree you're using, so you can still navigate the tabs normally.

I'm using vertical tabs since 4 years ago and to do so installed Tree Style Tab (https://tinyurl.com/y5gr4dyn)

Also has to disable horizontal tabs create or update the file chrome/userChrome.css located at your profile with

#TabsToolbar {
  visibility: collapse;
}

and add the setting toolkit.legacyUserProfileCustomizations.stylesheets with value true (use about:config)

Top right of my tab bar in firefox, there is a little down pointing arrow. I click that: BOOM vertical tabs. Now make it an optional fixed thingie and let me stack them. I may be missing something here, but that sounds like something an experience Firefox dev can implement in half an hour.