I'll continue my thread here, as there are more answers. Here is the original problem:
https://chevroletforum.com/forum/ven...70/#post517917

I still have not fully checked the VSS wiring, but I'm starting to think that the problem might be in an old capacitator on TCM or PCM.
The problem mostly happens when going uphill. It may disappear after turning on and off the engine. Here is how it behaves:
https://photos.app.goo.gl/vQrYjCRZWW2HuvrMA

One error that appears randomly (long before the current problem) is P0446 (issue with your vehicle's evaporative emission control system), can this affect the VSS thus making the gears shift when not needed?

 

At the end I replaced the whole VSS line up to the PCM (purple and yellow wires, pin 64 and 65) and the car runs smooth again.
It is still a mistery why releasing the gas pedal was making the sensor read correct...
https://chevroletforum.com/forum/ven...70/#post518199