How much stick drift is normal?
A perfectly still stick almost never reads exactly zero. The question is not whether your controller moves at rest, but how much and in which direction.
Noise versus drift
Sensor noise wanders. The reported position bounces either side of centre by a few thousandths and averages out to roughly nothing. Every analog stick does this and no game will ever show it.
Drift leans. The reported position sits away from centre and stays there, so the game receives a constant small push in one direction. That is the difference worth measuring.
Numbers to judge by
Using the 95th percentile of the resting offset: below roughly 0.01 is healthy, 0.01 to 0.04 is a minor deviation you will usually not feel, 0.04 to 0.08 is moderate drift that appears in slow aiming, and above 0.08 is severe and obvious in menus.
These are GamePadTestLab bands chosen to be useful to players. They are not manufacturer warranty specifications, and no browser reading can decide whether a pad qualifies for a repair.
What to do next
First retest. Temperature, a recently moved stick and an uneven surface all shift the result slightly, so run the measurement two or three times.
If the offset is repeatable, find the smallest deadzone that hides it. Plenty of pads with a minor offset stay perfectly playable with a 5% deadzone. Only when the required deadzone starts eating your aiming precision is it time to consider a stick module replacement.
Ready to check your own controller?
Run the stick drift test