> I love the idea of all application windows being able to be moved into tab groups. Are there window managers that do similar things?

Haiku Stack&Tile!

https://www.haiku-os.org/docs/userguide/en/gui.html#stack-ti...

A long time ago I implemented something like it (the stack part, not the tile part) in Awesome/Lua, so that floating windows could be tabbed together. Code is lost though. It was a bit too buggy anyway, pushing Awesome to its limits.