I usually get away just fine with Control+Command+f to fullscreen the window, and Control+Up will open up Mission Control so that I can get two fullscreened windows side-by-side. It's all built into macOS.

Windows 11 adds snap layouts, for which there is currently no analog, but this will let you do the side-by-side thing from earlier versions of Windows as long as you can tolerate the fullscreened windows becoming their own Space. (I actually find this preferable myself, but YMMV.)