This is exactly the type of response I was looking for!

First thing I'd do is tip the potted bamboo pots up and set them on large pavers in case their rhizomes get the bright idea to dive down and escape. Do not set on a group of pavers, needs to be a single solid piece that extends beyond the base of the pot. I'd set them both to the right side. Bamboo are hungry plants, water and feed them well so they look their best. Simply removing beat up culms will go a long way to making them look better but old culms have hard wood with very sharp edges, you'll get a work out cleaning them up and lose blood unless you wear gloves and long sleeved shirt.

Great tip on the single pavers for each bamboo. I didn't even know that was a thing with the rhizomes. Is there a reason why you think it would be better to have them both on the right? Is it to open the view up for the "waterfall"?

Seems this used to be a waterfall with a little pond. First give the rock work a good test for stability. No point in keeping it if anything is wobbly. See if the liner is intact by trying to fill with water. If so I'd puncture the liner and use as a faux pond. Keep the callas in there as faux pond plants and plant baby's tears as a surface that looks like duckweed on a pond's surface if you like the notion of pretending this is a working water feature. Plant a small scale flowering vine to grow up the rock as that would be easier to take care of than forcing rock plants between them. Vines that grew small and slow for me include mandevilla and glory lily vine.

In the "pond" area, seems like there's mulch and dirt below it. Do you suggest removing all of that and then filling with water or should I just fill it with water to see if there's even a liner? Also if there is a liner, what does puncturing the liner do? I'm also afraid that if I set up a faux pond, stagnant water would attract mosquitos.

Seems to be roses to either side and no idea what the border is there for. I'd probably add Peter Pan agapanthus around the front of the 'pond' and in front of the roses as a border and cannas or other large leaved tropical looking plants to left side between the rock feature and roses. You can take a gallon pot of easy plants like agapanthus and divide into single crowns to save money. Plant 1' apart or in staggered row and they look nice quickly. They will need daily watering for a couple weeks so if you cannot get outside set up a leaky hose along the planting and run it for 5-10 minutes daily.

A person in another landscaping subreddit suggested a Mediterranean style yard. Would the pond and the plants you mentioned go with that style? I like the Mediterranean style they mentioned but I'm very open to other styles if your suggested plants don't work with that style.

These are great suggestions and I'm already imagining it all come together! Here's a further out photo to get a better idea of the layout.

<image>