* Orion (mac only) - https://browser.kagi.com/
* Brave (mac, windows, linux) - https://brave.com/download/ (right click any tab and then Use vertical tabs)
* Arc (ugh) - https://arc.net
As an example: in the email client, the folders appear in the side panel, which is conceptually "above" (to the left of) the tabs. (I use English, and in English we read left-to-right, then top-to bottom.) The problem is that in fact, the folders are logically inside the mail tab: they only pertain to the content of a single tab, but they are shown for all tabs.
It is, IMHO, a design mess, and I have tried to convey this to the company, but it seems uninterested.
A second example of neglect of this L-to-R, top-to-bottom rule is GNOME. In GNOME 3 and above, action buttons in dialog boxes appear in the CSD bar at the top... but I have not yet read the contents of the dialog box, so I do not yet know whether I want that action or not. Logically, the buttons should be at the bottom, and grouped together, and this applies equally to R-to-L scripts (such as Hebrew and Arabic) or to writing systems that are conventionally and classically top-to-bottom _then_ side-to-side, such as Chinese and Japanese.
Orion is much more interesting in terms of UI and also in performance, but I have to say that tab management on Arc is superior, as it has the concept of "folders", not only nested tabs. Orion has something like this planned, but there's no clear date.
The solution you're proposing (kanban style) is intriguing and something I would find pretty useful. Might even make me switch to Orion back.
I switched from Orion mainly because Spaces don't share cookies and sessions with each other, meaning that I can have [Private][Work - General][Work - Client] and use for example Gmail in each of those with different accounts, without fear of switching to a personal/work one.
I also lost tabs in Orion when syncing multiple devices, which Arc has handled flawlessly. It's interesting, because they both use iCloud.