EGR leaks oil?

The car is 1.9 tdi BXE engine golf 5 2007, 193000 km

Noticed a check oil lamp on my car (I was thinking it was normal because it’s due for a service and it drinks a little oil, didn’t really notice a big loss of oil, I think I added around 100ml,

The lamp went away when the car warmed up (btw I live far north in Europe above arctic circle)

Anyways...

Later I thought to check under engine cover, and say oil, and it seems like it’s coming from the EGR valve from top and groups at the bottom to I think intake, at least the part after egr cooler.

Now this egr to my knowledge is water cooled so idk why there is oil there in the first place.

Thank you for any help.