Thank you Manush, I was looking for at the wrong place then....
I found smsdpprov.log. it was in another folder (in the new DP) but it was there 😉
The logs at my eyes are are a data tangle. How can I move and find what I need in those logs. For example, distmgr.log present in the Primary site is a large file and it grows more and more. Could you please sugggest me where to find a guide or tutorial where to start understanding how to interpret all data?