I tried Gtile on Fedora but found it wanting to emulate more of Linux's auto-tiling interfaces, which isn't what I want when using floating windows some of the time.
The Pop-Shell extension mentioned above was the best floating + tiling experience I'd used so far. Floating windows work like normal until you hit super+y where they'll begin to auto-tile & try to find sane spacing for the different windows onscreen.
You can cycle through those windows (and I believe resize them too) with keyboard commands, but also resize and drag around them with the mouse like normal. You can even drag them on top of each other to create "tabbed" windows behind one another with little selectors at the top.
I used this recently on a 12.5" (1080p) screen to reference Firefox on one half, while having my terminal, file browser, and text editor all "tabbed" on top of each other in the other half. Made it really smooth to fit all that into a small screen in a way that felt sane & easy to multitask with. I'd highly recommend trying that extension out and seeing if it can fill your needs, even if it's not 100% trying to fill Fancyzone's role.
