Diagnosis
The joystick is just stiff by design, and the OSD menu on the G6 has a known slight lag when navigating. It's probably not broken, just annoying.
How to Fix It
For the physical stick, press firmly directly inward (towards the center of the monitor) until you feel a definite click to select. To navigate, push the stick in the direction you want—it's not a toggle, it's pressure-based. Push harder than you think you need to.
If That Didn't Work
Download and install 'Samsung Odyssey G6' monitor drivers from the Samsung website. Sometimes this can improve communication with Windows. Also, the OSD is most responsive when the refresh rate is at its max. If you've lowered it for testing, set it back to 240Hz.
Heads Up
Avoid using the joystick with long fingernails—you can slip and scratch the screen. If the joystick truly feels stuck or unresponsive in a specific direction, that's a hardware fault and a warranty claim.