When quick menu is open I can select players, stickers, etc. with the same hand the quick menu is opened with.

For example when I open QM with left hand, the laser pointer is in the right hand highlighting and selecting players as it should.

Left hand doesn't highlight players right away. Aiming at a player with left hand and pressing trigger will select the player the same way the right hand does but without the laser visual. After pressing the trigger on the left hand will also cause the left hand to highlight players.