Starting with v4.636, BTT adds basic keyboard navigation to floating menus when shown via the "show / hide floating menu" action and the "keyboard focus" option enabled.
It should be possible to tab through items or use arrow keys, however the arrow keys will just be able to follow the direction of the flow (up/down)
Triggering the selected item is done by pressing enter.
Selected items use the same effect as when hovered.
Would be great if you could check whether this works for you