It appears like you already have a pergola for dining. To me, landscsping and natural shade is what you’re missing. For ideas, here is a video of ours taken last season

https://youtu.be/yh0ZL-PwsMQ

What are you missing? Flowers, shrubs, trees. Where would I put a screen porch? I'd want a good connection into your house, so, the inside matters. Consider light, as a roofed porch will reduce light into the rooms it is in front of. A fireplace to extend the season.

Here are some ideas, you can add an awning to the pergola shown: