(Not OP but...) A long time ago, I used Fluxbox which had a neat arbitrary window tabbing feature. Middle-mouse dragging one window title bar on to another created a tabbed window. There were keybinds for rotating through tabs vs windows.
I found it novel but with most WMs, I found myself basically doing a very small number of fullscreen windows per workspace. This led me to my current Sway/i3 setup which seems to be working pretty well. Downside is gkrellm, which used to live in the dock (OpenBox), doesn't really fit in the new world order.
It's almost certainly not what OP is using, but if you're interested in tabbing of arbitrary windows as a built-in OS feature, I'd suggest you have a look at how BeOS used to do that. You can still try it with Haiku[1].
I'm also fairly certain that functionality could be implemented with a handful of scripts in awesome (in a floating way instead of using pre-existing tiling WM features).
> Many tiling windows managers like i3 and XMonad have a tabbed layout
I'm aware of that - I use Sway on my linux machines, which ported that over from i3. But thanks for pointing it out, anyway :)
What I didn't know is that openbox and fluxbox can do this too, as oblio notes (but that's more out of disinterest for those two - maybe I should have a closer look).
I mainly pointed at awesome because I find it to be - well - awesome for being so flexible. You can do almost anything if you want to bend it for your specific workflows - be that in a tiling or floating layout.
For example: I still have a couple of scripts lying around that introduce the workspace behavior of the Gnome 3 shell in an awesome desktop.
BeOS did surprisingly little with its tab titlebars. It couldn't even automatically stack them. If you wanted to use them as actual tabs you had to hold down shift and manually move each individual tab to the right spot along the top of the window, and then manually move the windows on top of each other to sorta simulate pages being stacked. No sort of "drag these windows together and we'll turn them into tabbed pages" functionality which would have been convenient.
I find BeOS mainly curious because it experimented with strange features on each level (e.g. said tabs, BeFS/Tagging, etc). I think every one of those features should (and probably would) have gotten an overhaul by now if Be Inc. was still around.
That said, I haven't looked much at their APIs. If the tabbing behaviour is exposed properly, I can imagine it would be quite easy to write a small utility that stays in the tray and does that automatic tabbing separately.