I'm sorry for my late answer. Thank you for your help and for the photos. I haven't got any information about the Satellite brand.
Yes, you're absolutely right. This is definitely the same guitar. I made a bigger dig and it showed that this bass was sold 3 times between 2019 and 2024 (my purchase was the 4th).
One of the owners was the manufacturer of the recent pickups. It is a small Hungarian one-man brand, called Woodhead. IMO the manufacturer swapped the pickup for the self made one and possibly that was the time when he added the J-type unit. The bridge was original at this point. Later it was updated by the last owner, who swapped the original with a Schaller 3D-4 roller bridge.
The link you have posted has taken when the manufacturer of the pickup sold it, so it is his advertisement.
Thanks again for your great help.