> Tiling left / right etc? Doesn't exist

Sure it does - long press on the green maximise button and you get a little drop down. For me it includes "Enter full screen", "Tile Window to Left of Screen" and "Tile Window to Left of Screen". Tiling is like full screen but with two apps side-by-side rather than one.

If you want to maximise a window instead of going full screen (that is, make it as big as possible but not overlap the menu bar or dock), Option+Click on the green button or double click the title bar. macOS calls this "Zoom". Safari is atypical in that maximising it only changes the window's vertical height, but pretty much everything else maximises height and width.

All these options are on the 'Window' menu as well.