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.
I don't find the tilling feature useful at all and of course this is my personal gripe with tilling in general.
The last thing you want is having your windows perfect then ANY new window or dialog open automatically messes it up and you have to "re-organize" every time. Setting layout should be a one and done thing.
In the past, I used an extension called Put Windows that was perfect for my need, but that stopped working on Gnome 40.
I guess it would still work with 40 because of how simple it was, but even if not, it would most probably be trivial to update, so you might want to consider this route.