Pergola attached to the house (brick wall)

I’m considering building a pergola in the backyard. I have a two story house with brick veneer. Considering two options as follows. The pergola will be covered by a polycarbonate roof. 1. Pergola attached to the house without back posts 2. Pergola adjacent to the house with 4 posts

For #1, the pergola will be attached to the house using a ledger board that will be drilled through the bricks into the studs. There will only be two posts in the front of the pergola. No back posts as the pergola will be attached to the house. I’m worried whether this is a good idea for the structural integrity of the house/pergola as they both might settle differently.

For #2, the pergola will be a free standing structure with 4 posts, but adjacent to the house. Since it’s not attached to the house, there’ll be a small gap between the house and the pergola. I’m worried this will cause water to get into the pergola from that gap when it rains, limiting its usability.

In a dilemma what’s the best way to go here. Interested in hearing your thoughts/experience. I do not want to risk the structural integrity of the house and also don’t want water getting into the pergola from behind it.

Not considering a covered patio as it’ll reduce natural light getting into the house.

House picture

Edit: I live in Cypress and have clay soil. The yellow in the picture is concrete and red is the pergola.