Taking a guess here, from what I am seeing on the screen.

If you are allowed to add a tarp over the soil, then you can add an outdoor area rug over the area. Hopefully, this area drains well and you won't have a pool when it rains.

Adding an area rug will give you space for two chairs and a table to enjoy outside. It will also give you some nice color.

Then you can consider some large planters. Annuals will liven up the space during the summer.

Consider a couple of Adirondack chairs rather than a table & chairs. The arm of an Adirondack chair is wide enough to hold a drink glass and you would have a comfortable place to sit & read.

I would do some gardening bags where you get sun with some fresh herbs (if you cook) or some nice flowering plants-- people are even using IKEA bags as Gardening bags so other than the cost of planting soil its not too much $ and they are portable - in the area under the porch I would do some cute chairs and a table if you are planning on eating out there - as mentioned below Adirondack if you just want to sit- maybe an umbrella and some outdoor lights (solar or plug in if you have an outlet available) to brighten up the space

That’s a nice space!

What’d I’d do, if budget allows …

Use large pavers or deck tiles to make a seating area inside the bigger bed:

A portable grill:

https://nymag.com/strategist/2017/04/best-grills-portable-electric-weber-gas-charcoal.html

You’d have plenty of room for two chairs and a table. I don’t know your style … some examples:

In the rest of the bed, the other bed on the left, and on the current path, I’d have a few containers with plants that can take low-light conditions.

Trellis for interest on left side fence:

If there’s a way to have them, patio string lights would be nice:

Again, I don’t know budget, or growing conditions there, just some general ideas. And all easy to move and use somewhere else later.

Even though this isn’t a balcony, a good resource for ideas would be searching how to decorate apt balcony … lots of great inspiration for utilizing small urban spaces.

I see those metal railings covered in climbers like morning glories, beans, Cypress Vine, etc. depending on the amount of sunshine available. The wooden fence could also support plants.

Here are some layout ideas. The patio area can be gravel or other temporary surface. The plants shown are primarily perennials. How many you use is up to you. They can be planted in decorative containers, rather than in the ground. Annuals can also be used (ferns, impatiens, variegated ginger, begonias of various types, caladiums, etc.).

String lights are a great idea! I also love the deck tiles so I can make a little pathway to the center where I can put the little chairs and tables. Then I can put some foliage surrounding the area.

The left area gets a decent amount of sun so I’ll put some colorful plants for that area. Under the deck obviously gets absolute zero sun (hence the dirt and dying grass) so some foliage would work well. With that in mind, I’ll probably set the grill on the brick area so the smoke doesn’t go under the deck and bother the neighbors upstairs.

The photo was zoomed out to get the whole view, so there’s not as much space as it looks.

Are the deck tiles inexpensive and easy to install and remove? Any recommendations? Are they like puzzle pieces you just shove in the dirt?

Dig Dug’s design will not survive under the deck. You might get away with shade tolerant subjects like ferns in containers so you can keep moving them around to get periodic stays in more light.

Patrick, I’ve never used the deck tiles, but have been researching them for a project of my own. Just do a search, lots come up at various price points, as well as info on installation and such. I’ll be putting mine over dirt, too.

I'm guessing that if the existing hosta & other plants are living, then other shade tolerant plants will survive.