Opera 12.16 (the last Opera version) had both native support for vertical tab bar and toolbars (it already had it a decade ago) and a kind-of-okay "tab group" feature (groups of tabs could be collapsed so that they wouldn't take much space visually).

Unfortunately, they started from stratch with Chromium-Opera, and even after more than 10 versions it still lacks most of the great features of Opera.

Day to day, I use both Firefox with Tree Style Tab, and Chromium with Tabs Outliner. This isn't perfect: Firefox still takes a minute to load the session with 700+ tabs, and Tabs Outliner feels kind of a hack and isn't really integrated.