All items below are available in different sizes.

A retractable awning would make the most sense.

I think this company used to advertise on TV! https://www.sunsetter.com/

Splurge for the electric/automatic versions, so much easier to hit a remote button than have to use a crank!

Continue the roof of your screened porch over the patio.

I'd plant a tree.

First, we planted a tree to shade our deck - it takes years to get to where it offers shade so after about 15 years we did the retractable awning. It was crank because the awning company didn't recommend the motorized due to short life span but 2 years ago we added the motor and it is great. You'll have to do something about the wires. They're in the way

Allowing for the electrical, needing sun protection on the side and ensuring the back of house feels connected, suggest a white pergola with a drop down screen. It doesn’t have to be huge given the amount of seating you have. This one is sold at Rona if in Canada, but should be easily found in the US.

If better overhead sun protection is wanted, consider a model that has louvered slats, but not attached to the house. When sun is setting, the heat may not be as intense, but you could move your BBQ to the far end so seating is out of the sun’s rays.

On another note, be sure the posts are secured into the patio, so ensure posts have a base with holes to secure down (trust me!).

Perhaps something like this pergola frame with adjustable shades would work well at your home.

Perhaps others love these. If it helps, I really like the look, but are a pain to move back and forth (ours are not portable), the fabric bleaches/collects dirt, and when it rains if not closed, the water pools so you have to nudge it off. We do not open when really gusty and removing/adding every season takes a lot of time.

The retractable awning is probably most cost effective but does not address the surrounding patio from sun. A pergola would need to have shade at the top and sides to make it useful. Another option is an appropriately sized pavilion top (example below) then could just add roller shades to the sides to block sun when needed. As mentioned, extending the roofline from the sunroom to cover the area might be one to consider.

Also showing our pergola below and it provides virtually no shade (faces south) so it's too hot under there once we hit the 90 temps here in SC.

We had the same problem, and finally built a permanent roof over the deck. Best investment we ever made--it not only shields the deck from sun, but also provides shade to the living room which was blindingly hot and sunny in the afternoon. If the sun is a problem coming in the sides, you can get canvas drops, like they use in cabanas at beach clubs.

Pergolas don't block the sun since they have open spaces, which I would find very annoying. And trees take too long to get to the right size to block the sun.

We have some wonderful cantilevered umbrellas which we use to provide shade in our yard. They can be pivoted on their base, set at angles depending on the sun’s position in the sky etc. They are the only thing I have found which provides the flexibility to provide the shade we need at any time of year. Our pergola breaks up the sunshine a bit, but when the sun is low, is useless. All sorts of shades on pergolas can be hard to maintain and constantly adjust. If you do decide to investigate the umbrellas, you need to invest in a high quality one which has good structural integrity.

For patio shade, consider a retractable awning for flexibility—it’s great for adjusting coverage based on the sun. Pergolas with climbing plants like wisteria add natural shade and charm, though they take time to grow. If you want something portable, large cantilever umbrellas work well and come in stylish designs. For a budget-friendly option, shade sails are easy to install and provide good coverage, just ensure they’re securely anchored for windy days.

I think a retractable awning is your best solution. No posts to get in the way. You can adjust the extension.

Retractable awnings are very nice, and we have them on other windows in our house. But they don't hold up as well as a permanent roof in windy conditions--we have to retract them when it gets too windy. The canvas is nice but nowhere near as sturdy or long-lived as a roof.

I’ve been looking into different patio shade options myself recently, and honestly, it feels like there are endless choices depending on how much coverage you want and your budget. I was leaning towards a retractable awning for flexibility, but then I saw some great setups with pergolas and shade sails that look more integrated into the backyard space.

One thing I noticed is that the direction your patio faces really affects the type of shade that works best. For example, in our case, the late afternoon sun was brutal, so we had to prioritize side panels as well. Definitely worth considering how the sun moves throughout the day in your yard.

On the right you can see the roof we added to the back of the house, which faces west.. Also added an awning on the south side

Just to note--having the back of the house facing west is not optimal. But when we were looking for land we had no choice in the area we wanted.