DIAGNOSIS The 5-way joystick/navigation button can get stuck in a slightly depressed position from dust or debris, or its internal microswitch can become overly sensitive, causing phantom presses.
FIX First, let's try a deep clean. Power off and unplug the monitor. Take a can of compressed air and, with the nozzle a few inches away, give a few short bursts directly at the base of the joystick. Tilt the monitor to help debris fall out. Next, use a cotton swab very lightly moistened with >90% isopropyl alcohol to wipe around the joystick's rim. Don't force liquid inside. Let it dry completely. This often frees up any stickiness. Plug it back in and test. When using it, press directly in and release fully—don't rock it side-to-side while pressing.
IF THAT DIDN'T WORK The issue might be electrical. Check if the phantom menu pops ups are tied to a specific event, like turning on a desk lamp or another appliance on the same circuit. If so, it's interference. Try plugging the monitor into a different outlet on a separate circuit if possible.
HEADS UP If the joystick is physically damaged or the random presses continue after cleaning, you'll need to contact ASUS for service. The joystick is part of the main control board, so don't try to disassemble the monitor yourself, as you'll void the warranty and risk damaging the panel.