Hi Michael,
I did "keep separate" which helped a lot.
But now I have issue that I want to join those two objects (extruded side and original model) and when I do the command it seems like it's working but it will not join.
EDIT: found out that the big original object has issues performing booleans with other objects.

I also tried overlaping the objects with 0,01mm but didn't help.

Any idea why it won't work?

I can send you 3dm file but I would like to avoid people doing things for me.