It was cheap enough to buy from AliExpress another unit. Although the seller said it was brand new, I believe it was a used unit.
The left and right seats should have different part numbers. This car is a left-hand drive model, therefore the mechanism was on left side. It has height adjustment only at driver's seat. The article/part number for the mechanism is 1J0 881 053 D ( 1J0881053D )
This probably applies to few other MK4 models and a very easy to change item.
First you have to remove the handle. Unfortunately I did not take picture of this process. It is in place with 2 torx screws. You can use a very thin screwdriver (and I mean a really thin precision electronics screwdriver) or a carpet knife to patiently pry the caps out. I read that some people drill them and replace with new ones. This is not necessary if you have thin enough tools.
The second part to remove is the seat back level adjustment knob. I also read that many people break it when removing. However there is an easy way to remove it. If you look from behind the seat, you can see the tabs holding the adjustment knob. You only need to lightly pry the tabs one at a time and pull the adjuster out from other side. There are 3 tabs. You will need to patiently turn the knob a little bit for each tab and make sure to not press them back in.
Here is a photo from how it looks like from behind. I marked where the tab is with the red arrow:
But in case if you break this part, you can get a new one from AliExpress for few euros only! The part number is 33D 881 671 . Below is a photo from how it looks like inside. You can clearly see the 3 tabs in the photo:
Next is to remove the screw from the front of the seat and also the screw under the seat distance adjustment handle and remove the handle. The front middle screws are philips screws but the handle screw is again same size torx screw. Unfortunately I have removed the screw already when I took the photo below:
Below is a photo from under the seat. While this is no use for us, I marked one of the plastic tabs holding the side of the cover. there is an identical one on the other side and you need to unlatch it when removing it.
One thing else to remove is that near the middle is a hidden plastic tab. I didnt realize this was there and I could still remove the plastic cover. But I recommend first removing the tab. You can see it in the photo below. It is just pushed into the hole and you can remove it by pulling out.
I also marked the various plastic tabs holding the part in place. You should take care to not break them.
Now all the screws and handles are removed. You should start taking the part out from the front first towards the back. I managed to get it out by wiggling up and down mostly. It requires medium amount of force and careful flexing of some tabs. Especially one tab on the upper side needed a little bit flexing to get the whole thing out.
In the above picture, you can also see the nuts holding the adjustment mechanism. It is in place with only 3 nuts (I think they were 10mm nuts). Before removing them, if possible, I recommend lifting the seat up to highest position. This is because the seat incorporates a very strong spring to help lifting the seat up. So if you remove the mechanism when the seat is down, the seat may jump with the force of the spring. When the seat is all the way up, at least for me, the seat just stayed in place.
So, after removing those 3 nuts. I simply wiggled out the adjustment part and inserted the replacement one in place. Then I had to turn it a little bit to align the holes to match.
The assembly is simply the reverse of removal. Take extra care to not break the plastic.s