I had a similar issue. Deck is nice but if termites are a problem, pavers are nice too. My small yard was almost exactly like yours, if you replace the fence view with the back of a brick garage. I wanted an oasis too. So here's how I approached the landscape design. Up close to the house, patio area was used for outdoor dining because the patio was adjacent to the kitchen door so we ate outside very often and also I ate breakfast out there in the AM. So my goal for that area was something nice on the sides to look at while dining but not too obtrusive because we needed the space for the dining table. We also occasionally entertained out there, so we had two extra chairs we could pull up to the table or arrange easily for other entertaining seating configurations.

Back patio area I used for lounging, relaxing seating in the evenings. We had a swing and sat out there often in the summer after the sun went down do it was cooler. In the middle of the yard was almost like a doorway or archway, with two side garden jutting out designed to be viewed from both spaces. The garden that we viewed from the lounging area had a lot of white flowers and some night scented ones.

I don't have access to my photos, but basically think of it as two rooms with the plant landscaping in the middle to create the separation, and the views. We had a small fountain in the middle which provided a focal point in each direction.

You can add planters to the fences or art or trellises with plants growing up on them. I grew petunias in planters for color and scent, a rose for view and scent, and red raspberries for fun picking and putting on my morning cereal. YMMV, think about what you want to do and see out there.

It looks to me like you have 2 disconnected squares and a back door with no path/mulch path next to concrete. Do you need both squares? If not, consider removing one of them. Otherwise, you need to connect the with a path.

You took you pics late orr early in the day, making them look dark and shady. You might want to take some midday pics and tell us about sun and shade.

The Brits have lots of small backyard oases. You should look at some of their ideas. Particularly how they connect rectangles. Some have the grass bordered on all sides, others use a path. You need to decide the structure and tell us the zone and sun/shade if you want planting advice.

https://www.houzz.co.uk/photos/garden-ideas-and-designs-phbr0-bp~t_10323?fi=80

This is not a great photo of my yard, because the back area against the garage had not yet been landscaped well. But it kind of gives you the idea of how the area was divided by the garden beds to create two "rooms" each with a view of the garden around the small trees. That's from my second story. I eventually pruned up the trees so you could see through their canopy. They were just getting started in this photo so I let them grow a bit before limbing up. This was before we installed the fountain, which was below the red tree. The red tree was a stunning fireglow japanese maple that died. We replaced it with a smaller maple in a pot. The gray brick was probably not the best choice but what we could afford. I should have done a wood deck but didn't think it would meet code, I was a landscaping newbie.

https://youtu.be/lOAwXzKfTxY

This link shows our patio. Believe ours may be larger than your space but the basics will be similar. For thoughts:

Shade and sun.

A place for both intimate and group dining.

One for conversation.

Grilling

Possibly relaxing by a fire.

Lighting

Water feature

Landscaping - we went with a softened style landscaping to contrast with a geometric paver patio. A nursery designed the gardens because selection of and plant placement is important. Were the bistro table now sits was initially a hot tub.

Hope this helps