USB vs Bluetooth for controller testing
The same controller can produce noticeably different readings depending on how it is connected. Here is what actually changes, and what does not.
What changes
Update frequency and jitter. Bluetooth schedules data in slots and shares the airwaves with everything else nearby, so the intervals between updates are longer and less even than over USB.
Optional features. Vibration in particular is far more likely to be exposed to a web page over a wired connection in Chrome or Edge.
What does not change
Stick drift is a physical property of the stick module. A drifting stick drifts on either connection; only the sampling quality of your measurement differs.
Buttons behave the same way too. If a button fails to register over USB, the connection is not the reason.
Practical advice
Test over USB when you can, especially for drift and update rate. Use a cable you know carries data, not a charge-only one.
Then run the same tests over Bluetooth and save both reports. Comparing them is the quickest way to tell whether an input problem is the controller or the wireless link.
Ready to check your own controller?
Measure your update rate