I think it looks unfinished because it runs off into nothingness at the patio edge. I'd want some kind of a border around it. Either a hardscape edging or a flower/shrub border would do with an opening for accessing the rest of the yard. And I'd want to paint the Adirondack chairs to blend with the rest of the furniture and move then near the other furniture for a conversational group.

Plant appropriately so you have shade during the hottest part of the day. Nothing beats the leafy shade of trees. Small trees to S/SW.

Here are some thoughts:

Yes, garden around the patio, including one of two flowering native trees a little bit out from the patio. I would also move your seating out away from the steps and house-if you must have something in front of those steps, I suggest potted plants/flowers. Once you get plants in there it wil look wonderful!

Try this...center a large outdoor rug on the patio and place the furniture on it, or at least the front legs of the seating.

They make rugs that let water run thru when hosed down. A lot of indoor/outdoor rugs absorb water.

I think it will look great once the sod is in. I would set some large flower pots around the edges in a few places.