SUCCESS!: How to make a new key incl. transponder
There's a little confusion there, mostly just with the names.
Firstly, there's 2 separate parts that need coding in each flip key remote, both with a separate process/system. One is for the immobiliser (transponder chip), and the other is for locking/unlocking the doors remotely (remote transmitter).
The bit mentioned that was re-soldered is actually the 'transmitter' for the remote lock/unlock system, and will need to be programmed in with a VCDS if the above quick method doesn't work (or you can't make it work without 2 keys, etc.). It's good to do it with this VCDS method as you can 'erase' any other old remote pairings, and have yours as the only remote that can unlock your car. There is also a max number of paired remotes, which sometimes causes issues programming a new remote from too many old remotes programmed to the car, and erasing/clearing fixes that issue too.
The other bit, that is actually the transponder chip, is actually the tiny glass capsule that's glued inside the casing of the remote transmitter, and interacts with a radio frequency ring around the key barrel, and like mentioned, if it starts the car, and no other keys are near the key barrel, that is already paired and working fine... This is the same for standard and remote keys.