Tiling window managers are great and I admit they gave me some inspiration for this project. I just don't find myself needing to have windows be split screen very often, at least not more then two. The one exception to this is terminals which I usually keep in a separate virtual desktop but besides that I would rather have the window I'm using be full screen.
Tiling window managers typically allow you to configure that. For example with XMonad (what I use, on Linux), you can set it so that all new windows are full screen by default, it's just a line of config like `layoutHook = fullscreenFull Full`.
You can also set any number of standard layouts that you like, and toggle through them with Mod-Space. So full screen could be the primary one, two-pane split screen the secondary one, all windows visible be the 3rd one, etc.
And as others have mentioned, using this in conjunction with virtual desktops is quite powerful. E.g. moving windows between desktops is just a key combo and is very quick, so it's easy to switch between full screen and side-by-side of any two tiles just by moving one to the same desktop as the other.
Try Niri or PaperWM. A scrolling window manager.
I think 90% of peoples issues with window management can be solved by using workspaces intelligently. I won't prescribe a specific method, but I personally keep certain things on certain workspaces. Browser on 1, dev on 2 and 3, chat on 4, music on 5, misc on others. I rarely need to use more than 5. And then I have bindings to go straight to these workspaces(mod-number keys).
My personal hot take is also that most people who think they really need another monitor are just addressing these symptoms because they're exhausted by alt-tabbing through 15 windows. They would be more productive on a single screen with a nice workspace configuration, though there are of course plenty of good reasons to want multiple monitors.