I'm also struggling with a macbook for work, but hold your mouse over the green circle in the top left for a few seconds and it'll pop up. (You don't get the nice snapping that windows does though)
I don’t see options for thirds, though. Even on an UltraWide monitor.
Holding option while hovering gives you more placement / sizing options too. If you click and drag a top bar to the right or left it'll snap to the right or left half of the screen. Dragging it to the top or double clicking will snap it to full size. Dragging to corners will snap to quarter.