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A bit attraction of _tiling_ WMs is ... automatic tiling of windows. Does Gnome do that (haven't used it seriously in about 2 decades)?

No, it does not natively, but there's discussion to do that [1].

There was a discussion here about it a few days ago [2].

popOs's distribution of gnome includes a tiling plugin that will work nicely out of the box if that's what you like.