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This looks basically like Tree Style Tab for Firefox only without the nesting of related tabs.

When you add "groups" (e.g., folders) it is magical.

TST is great, but it's nothing like Edge vertical tabs, which contain exactly the right amount of functionality for zero friction use. I have tried to get the same effect in Firefox, Vivaldi, pretty much anything that isn't Edge, but I keep coming back to Edge because it is so central to how I use the browser at a basic interaction level and, simultaneously, so simple to use that I can put up with (and deactivate) the other annoyances.

Brave has vertical tabs built in nowadays (though they're behind a flag, but they're more or less mature now), designed in a very similar way to Edge's.

https://imgur.com/a/dAAysvy

I recently started using vivalid, which also has vertical tabs baked in. I tried some firefox browser extensions but I find them to be really sluggish and feel tacked-on.