Attach the pergola roof to the rafters of the house roof

This is what it looks like from below, directly screwed through the bottom plate into the rafters.

Lamps are also mounted there, everything could stay in place.

For you, it would just be made of wood.

You wanted to put supports underneath anyway.

I also wouldn't make any holes in the ETICS.

With us, the wind zone is 4 and the snow load zone is 2