Figure out what type of sun control you have the budget to install.

We are in northern CA and guessing you may be in southern CA--but here we have had good luck with our south-facing yard with a center umbrella for the table (and soon will get some chairs for a new sitting area with a side umbrella) and large, deep containers. Tomatoes do beautifully in the direct sun. Our kitchen is on the inside of our patio wall and we actually don't have heat at all in that room because the direct sun heats the space so well (sometimes a little too well!) Our neighbors (whose back patio has the same orientation as ours) recently put in a new deck and built a trellis top over it like Beverly's third photo. It was crazy expensive but it does seem to filter the sun very well.

You can’t fight Mother Nature. Well, you can but you won’t win. Is that a concrete pad? Even worse.

Construct some shade. Shade sails (check Amazon) aren’t too pricy but you’ll have to figure out how to hang them sturdily.

Thank you all for the comments, looks like permanent shade is the key. So here is a follow up - we already have two pergolas, my husband thinks it will be too much /matchy if we add a third. i added more pics

Where in California ? There are wide variations in climate & maximum / minimum temps. My home at beach has temperatures in the 60’s & 70’s year around whereas my second home in La Quinta has a wide range of temps depending upon the season.

It's too bad the pool pergola is so far from the patio. It will be worth your while to move it onto the patio, or remove it and build one on the patio. Having that useless, sun-blasted patio is just a shame.

Have you found that the pergolas you have work? I think an awning like the ones shown that are motorized are the best for this type of situation since IMO you still want the light for inside.