Four of the six work on their own. You have to write the other two.
The common read: a <div popover> behaves like dialog.showModal(), so focus moves inside it, focus is trapped while it is open, and a screen reader announces it as a dialog.
Four worked and two did not, and the two that did not are the pair you were most likely to skip. Top layer placement and ::backdrop are unconditional: the attribute alone put the menu above a sibling carrying z-index: 2147483647, measured as a pixel and not as a hit-test, and a ::backdrop rule painted across the rest of the viewport in the same frame.
Light dismiss and the close request are on by default, and you turn them off rather than on: choose popover="manual" and both go, in all three engines, which is what choosing that value is for. The popover attribute ships in every browser, but support is recent enough that you should check it against the oldest browsers you support.
Focus is the behaviour you have to write yourself. Open a <div popover> and focus does not move: a button that had focus before the open still had it afterwards. Put autofocus on one control inside and focus moves to that control. Focus is not trapped either. showModal() makes the rest of the page inert, and showing a popover does not, so Tab can move focus out of an open popover and into the page behind it.
Implicit ARIA does less than the name suggests: the attribute grants no role at all, ever, and the invoker relationship the guides describe comes from popovertarget rather than from popover.
Write popover, keep the four behaviours it gives you, and then write the other two: autofocus on the first control that matters, and the role and label the element would have needed anyway. Those two additions are much less code than the component you are deleting.

