If the back end of the pergola is resting on the roof, there is danger of damming roof drainage, which would cause water to run under the shingles. You should explore if this is the case.

Based on the area shown in the photo, I'd be inclined to pave the whole area (everything from walk on back). It looks just right for a couple of chairs and container plants. IMO, there is not any place good for bed against the house, unless the walk were moved away from the building, but I like that less based on what I see here.

When you first thought of filling that gap between the two wings of your house, what had you in mind?