The mistakes are that I can hear the sound of sliding the finger quickly when removing it properly (I don't really slide it between notes, it's a minor slide while removing the finger) and the sound of the string being gently played while removing the finger.

I don't notice those sounds when playing without a pickup, so it's new stuff for me. If I play with a mic, would this sensitivity be reduced? Is there a solution with a pickup? I'm using a simple sound editor, and I managed to equalize in a way that those mistakes were reduced, but they are still there. I'm wonder if I will have to upgrade my skills to be more silent, or if it's not my fault, but from the pickup.