The first ingredient would be Tree-Style-Tab addon, but the horizontal tabs are also still present, and meant to be non removable as of mozilla.
The final step is then to go customize toolbar and force the tabs to the right so far that they disappear completely by adding in icons and flexible space bars.
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Interesting! Is it for wide screens?
I think yes, because you can pack in as many flexible space bars
as you need…
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EDIT: The Sideberry addon is even better to use than Tree-Style-Tab, here you have shorter access to switch views from bookmarks to tabs, and also Sideberry skips to tabs view automatically
EDIT2
… weeks later …
in the end, gave up the horizontal tabs because it is much more simple to have the tabs on the top and bookmarks on the left, there is no need to switch between those, so sorry Mozilla
you did it well, won’t call for vertical tabs anymore 
, thanks for the update sad that it didn’t work out. I am aware a few new browsers like Orion (not yet on Linux) also got horizontal tabs as an option but personally never really found an use for tabs on the side as I launch most things from Krunner or on mac from Spotlight or on Windows from the flow launcher 
and they also do navigation
You are totally right, sometimes one finds out by trying only, that some hype features are not so cool after all