That pattern — full right when the stick is centered, and neutral when you push it left — points to a hardware offset in the right stick, not just a software setting, especially since recalibration and a console reset have not fixed it.
1. Confirm it is the controller, not the Switch. If you can, try another controller on the same Switch, or try this Pro Controller on another Switch. If only this controller drifts, the fault is in the controller.
2. Recheck calibration carefully. Go to System Settings > Controllers and Sensors > Calibrate Control Sticks, then move the right stick slowly through its full range and let it return to center on its own. If the center position still reads far to the right, calibration cannot correct a worn or dirty stick sensor.
3. Clean around the stick base. With the controller off, tilt it so debris can fall out, use short bursts of compressed air around the base, and rotate the stick gently. Do not force the stick or flood it with liquid cleaner.
4. Check the live stick output. Connect the controller to a computer and open the free browser-based tester at GamepadTesterPro — https://www.gamepadtesterpro.com — then move the right stick slowly and watch its resting value. If it sits well above center at rest, jumps, or does not return smoothly to center, that confirms hardware drift rather than a dead-zone setting.
5. Decide on a lasting fix. A larger in-game dead zone can mask mild drift temporarily, but a stick that reads full right at rest usually needs the right analog stick module replaced. That is a common Pro Controller repair, but if the controller is still under warranty, contact Nintendo first rather than opening it.