That concrete looks like it just needs a good pressure washing, you can rent one for $50 probably at home depot (not sure what state you're in). it would probably take 2 hours. As for the garden, figure out what plants are thriving and remove ones that seem to be heavy on wood and low on leaves, they are likely past their prime. Id need a more detailed list of plants to help you. After that, just try cutting the planting areas larger with a shovel and bring in some higher quality dirt, a barkdust / soil and rock yard should be around that can deliver a couple yards of that to spread into your planting areas, then just pick out some plants and go to town on it.

I'm picking up the deep south from what looks like ruellia, oleander and ligustrum on the yard side corners of the patio. What your grandparents are going to need to actually use the patio is shade and a nice breeze. To that end you would need to build a pergola over the patio or go more modern with an easier to install shade sail.

After shade you just need to clean the thing up. Power wash the slab, clean the furniture, tidy the shrubs and weed the ruellia beds if needed. Toss the junk. Give them some new potted plants for the patio and put the bird bath back up. Depending on how much or how little they want the neighbors to see, you might need to plant a few walls out along the property line.

Once all that is done then you can plug in the TV and fan.

With the pictures given, we can't really tell if there are bigger problems that remain unseen.

Keep in mind as one option that there are durable epoxy coatings for existing concrete that can change its look dramatically.

Thank you all for the advice!

I’ll upload some more pictures of the backyard to give a better view.

Indeed we are in the south. I’m going to rent the power washer this weekend. As far as the plants, I’m going to get a list of their interest. I know zero about plants.

I had to look up a shade sail and pergola but i like them both! Probably start with the sail. Likely easier for us to install. My grandparents love their privacy

The concrete set is very nice - can be uncomfortable - have cushions been used? If not, could it be placed away from the patio, to invite people under the shade maybe, or in the sun with umbrella.

Then on patio if tv and action, lightweight moveable chairs ?

Just another thought. After you get some shade up and the patio all clean and comfy, go out in the yard and start a tiny little vegetable garden. Start small. You could grow some tomato, pepper and plenty okra easy enough. What is your grandmother's favorite vegetable?

I’d love bring some joy to my grandmother by making this porch apart of family gatherings again.

The answer is food. Home grown is the best kind.

Likely, you would want to place screening plants for privacy, not near the edge of the patio, but near the edge of the yard. There's no point in screening one's own yard from one's self.

Better view

That's a better view but not a complete one. We have blinders on here. You should return to the exact spot where this photo was taken and add two more showing the left and right flanking space, overlapping slightly with the above photo. (If you change camera locations, the photos cannot properly overlap and be reassembled into a panoramic scene, which is what we're after. (But not a computer generated panorama.)

Where does the walk go?

Sidewalk

Another option is to deck over the concrete, depending on the elevation of the back door. You can set 2X4's or 4X4's (PT) directly on the concrete slab and deck over it. This could easily be a DIY project and cost hundreds instead of thousands to give the patio a new life. I agree that a good pressure washing could be a simple solution as well. Look into concrete stains and paints. All of these solutions increase maintenance, expect pressure washing. Good luck and show us after pictures.

Depending on sun heat, and how many you entertain: could have concrete all the way.. to under the windows and place table set / umbrella there... unless near there you'll have a grill..

and lightweight chairs near doors, where people might eat, and move around...

A pergola would be a great added feature! And louvered wall panels is a fantastic way to get some extra privacy. Would you be at all interested in something like this?

Be careful to get grandparents approval for every action you do. Something you or I might throw away may have special meaning to them. Don't dig where a dormant plant might be. Plans and stakes in the ground can help them understand what you propose. Take your time, old people can feel overwhelmed.