The Vivaldi browser has a similar feature (not open source unfortunately). I've used it for a while, I quite enjoy the tab and bookmark management sidebars.

Just took a look, and it seems like Vivaldi has vertical tabs, but the similarities end there, it doesn't seem like it does tree-style tabs? Just has groups + one level of tabs...

Try Arc. You won't be looking back.

I'd love to but it not being available on Linux and invite-only both makes it very difficult to even give it a try :)

Arc being such a generic term it'd be helpful to include a link or explanation what that is.

Just search for “arc browser”.

https://arc.net/

Why? It’s based on chromium anyways. Might as well use Vivaldi instead.

They don't have sync for most things.

Firefox is nice in that not only it has sync of basically everything, but you can run your own server for it.

FWIW, I just tried Arc on Windows, but it seems like it doesn't do tree-style tabs at all, unless I'm missing something obvious?