I would like to make this corner a place to relax and privacy. Not spend more then 100.00.
You could add some tall plants/trees
That looks like a perfect corner to hang a hammock across it. Then in the absolute corner you could build in a table to set a drink and a flower pot etc.
You could set a pole and run curtains. Add lattice would be another option. If you want it to be large, you could run privacy curtains from the existing pole.
I would use bamboo plants to create a privacy
Obviously plants & flowers - get perennials that return yearly so you don't have to replace them. Pavers for a flat area. You can frame shower curtains and hang them on the fence for artwork. A shade sail will give you shade and privacy from people looking in from other yards.
There are lots of privacy ideas here:
I don't know what is on the large black pole in the center of the photo, but if it is tall enough, you could run a clothes line from it to the two sides of the fence. Outdoor Command hooks will keep it the height you want if you can't screw into it. Keep the line very tight or use a PVC pipe set in sand in a bucket to hold it up midway between the pole and the fence. For the privacy, hang some gauzy curtains on shower curtain hooks. Weight them down, if necessary. You can even string a line of twinkle lights if you have access to power. Inside the 'nest', you can place a comfortable chair on a small outdoor rug and decorate with plants or wind chimes or whatever suits your taste.
Set up some cheap reed fencing or the fake ivy panels. Add twinkle lights and lots of potted plants and flowers. Arrange some seating and a coffee table
If you choose to put in bamboo plants, they are an invasive species, to prevent them spreading put them in containers, they would look lovely. Another thought is Pampas grass, also put it in containers.
You can also buy cluster/clumping bamboo. It does not spread. There is a nursery in Davis, CA. They ship to you.
See if anyone is giving away pavers/ flagstone on a local yardsale site. Or create a simple gravel patio.
Try a hammock or a couple chairs with a diy patio end table between them, maybe a small fire pit.
Consider creating a shade sail that mounts partly on the fence.
Create a trellis planting area with easy growing vines for a natural wall.
Use dropcloth to create outdoor privacy curtains.
String some lights. Mount some solar lights to the fence.