I also had a left joycon, so thanks to everyone who commented about the difference with the battery screws.
After I closed everything, i could feel the battery moving inside, I think it'd be better to stick it in place woth some tape.
Also, the hardest part for me was stel 6, inserting the new cable into the tab. I couldn't make it stay inplace. Then I broke the black tab lock. But finally I managed to put the cable into the tab, fold it like described and close the battery compartment, and the cable stayed in place.
The joycon works! I hope that shaking the joycon won't free the cable as nothing is locking it in place except for the cable tension due to it being folded.