Full screen and split screen have become my default modes of using almost everything on macOS. It's a pleasant, generally better focused, way of interacting. I just wish it were richer like the tiling WMs I used on Linux. Maybe not as useful on a laptop (due to screen size and my aging eyes), but when attached to a high res monitor it would be nice to be able to split the screen into quarters, at least, instead of halves.
This is also what I generally want and we're not alone. There are a few active projects to facilitate this. Personally I like <ahref=https://freemacsoft.net/tiles/">Tiles</a>
ummm, how? When I hit the green button for full screen, it takes over the screen like a Spaces screen. How are you able to have side by side full screen of 2 apps. That seems like you are breaking the definition of the word full. If 2 apps are "full" screen side by side, you either have "half" screen views or 2 monitors.
Open Mission Control and drag a window into an already full screen application. You can also drag two windows in a new full screen space, or drag a full screen space into another to merge them.