It is hard to tell from the picture, but it looks like you might have a row of Pygmy Date palms under the windows. if that is the case remove them now while they are still small. They will very quickly get too big, block the windows and rub on the house damaging the stucco. The single larger specimen palm in the right corner is ok.

Otherwise that space calls for a mostly low plantings scheme and what you need is some color. Ti leaf would be a good taller, vertical element for between the windows and next to the patio.

Short plants to consider for that bed are bromeliads, aloes and other colorful non-cactus succulents. Shrimp Plant, Justicia brandegeeana or similar would work.

Ground covers for the palm bed off the patio to consider are Blue Daze, Evolvulus glomeratus or Oyster plant, Rheo spathacea.

I can’t help with specific plants, but giving the whole bed some crisp edging and removing the grass under the plants will give everything a tidier and more intentional look. Then plant ground covers and use mulch between them until they have filled in. Foliage color and texture will be useful as it provides long lasting interest, with flowers or ornamental fruit adding shorter seasons of interest.

In both pictures, it's a very odd arrangement using palms as not only the prime plant, but then also as a "groundcover" or backing "hedge."

In the first picture, I'd move the largest palm forward (toward the camera) and line it up closer to the center of the backing wall, planting its center at least 3' from that wall. (My red arrow vaguely shows the direction ... not the exact location.) Then fill in the rest of the bed with a groundcover, which might be Liriope or something that gets about that height. I would delete the palm at the near side of the walk.

At the other location, keep the two large palms and get rid of the backing row of multi-trunk palms. Create a bed of low groundcover (12" height or less) around the large palms, that extends to the patio/carport.

Instead of looking at the yard piecemeal as these two pictures do, It would be better to evaluate the entire back yard as a single entity.

There hasn’t been much discussion of function. Do you need the privacy screening provided by the current arrangement? Or do you just want something attractive to look at and don’t care about what is beyond it when viewed from inside the house?

I’m extremely late to respond and for that I am sorry. I do appreciate everyone’s comments! For the time being I have only added flowering plants to the area, but the area will be ‘fixed’ after a pool installation. (I never knew I needed one until COVID-19).