Hi Shaadal,
I normally faced issues with other buttons receiving inputs when changing the conductive film or conductive pads of the device. However, these were rectified by properly aligning the film and pad to the controller's base. Since the analog stick is separate from the L2 position it is tricky where the issue is.
Is the film and silicone pads clean, is there any dust on the analog stick, is there any blown-out/cracked components you can see on the motherboard of the controller?
If the inside of the controller is all clean and the mechanical/electronic parts look fine then you could have a shot at replacing the analog stick. Not sure if it will solve the issue but could be worth a shot. Is the L2 button press always registering in one direction of the stick or all directions?
You could also connect your controller to the PC and check this by going to this site:
https://hardwaretester.com/gamepad