How do I get shade over my patio without making it too dark inside?

A pergola was going to be my suggestion. It's not a solid roof so it lets light through.

The structure you have would not carry the weight of a pergola. You would need to install separate posts. A pergola with the sun sails would give you added shade but not block all the light.

YES

Google Deck Sails. Millions of options. Reasonable, removable and changeable.

Just an observation - your current structure isn't sturdy enough for Wisteria and probably not strong enough for a climbing rose. You'll need a lot more support than 2 x 4's and eight foot spans of lattice.

You could try a fast growing vine over the top. If you put string supports across for it to grow on, you should have a leafy sunshade by summer.

We put up rope lights on a timer. They have worked for over a year and are very cheap at amazon.

https://www.amazon.com/s?k=rope+lights&i=garden&ref=nb_sb_noss

I built a strong, permanent awning support around my patio using galvanized aluminum plumbing parts. The supports were either sunk into quickcrete or drilled into the patio deck concrete itself. I planted trumpet vines at the "entrance" posts to that area. They grow extremely fast and I trained them to go up and across all the top supports.

This allowed dappled sunlight onto the porch along with any breeze. The flowers were beautiful AND I had hummingbirds all the time. The even built a nest right next to the chair I always sat in!