Hover over the green stoplight, you get a popover with fullscreen options.
Press Option and the fullscreen options mutate into snap left/snap right/zoom.
These can also be found in the Window menu. Again, press option to mutate the fullscreen ones to snap.
And since these are menu options, one can set any keyboard shortcut of their choosing through the keyboard shortcut prefpane+.
So it is not "snapping" in the sense that you drag the window to the left or right side of the screen, and I would 200% agree that it is completely non-obvious to discover, but it is there for any one to peruse without any third party tool.
+ See here for how to achieve that, section "Tiling and snapping" (along with more things to make first party things more sane for a certain crowd) https://lna7n.org/2021/04/16/a-survival-guide-to-macos-from-...