Does it show on the diagram where the drain that is dumping water is located? You don't want a hard fall, you want a gradual fall of the water otherwise it will erode where it exits the drain. You might have to create a wide rock swale to create a gentler pitch.

In the diagram above you can see the drain at the 'opening'. There is gravel at the bottom.

The water is going to flow straight down from where it comes out of the drainpipe. It may not flow into that entire area, hard to say because I can't really see the topography of the whole area. You want as gradual a flow as possible. Are those oval things rocks? Because if water flows through that area, it's going to flow between the rocks and under the rocks and erode some of the soil. Not that the rocks are a bad idea, just prepare for that. A "rain garden" is at the bottom of the hill, the flat area where the water eventually stops flowing and ends up standing. Ask me how I know . . . Or better yet, take a look at my baby . . . That whole area had to be landscaped to tolerate water flowing through it. The dirt at the bottom is the area where the water mostly gets absorbed due to the slope leveling off . . . some. But the whole hillside needs to accommodate the water flow to some extent.

If I had to plant it over again (no time right now for the "after" photo) I would have bought one of those wildflower mixes designed for such a site, and seeded the whole thing as a wildflower meadow. Can always go back and insert some shrubs. But I'm fighting deer along with water, so my vision of a mix of shrubs and wildflowers and grasses has been hard to achieve, but it's not all the water's fault.

Adding that you may want to put some kind of meandering landscape cloth and rock lined "stream" through the garden to try and channel the flow of the water. Then plant around that. The topography and water do what it will do, you hard engineer that first. The plantings just decorate it and tolerate the conditions.

Yes, we have all that we need for the hardscaping. My original post is about plant layout. :) These are the plants which have since changed (of course!):

11 Karl Foerster
7 Ascelpias Incarnate-straight species
15 Liatris spicata -straight species
15 Echinacea purpurea -straight special

11 Sporobolus heterolepis 'Tara'

The contractors also drew a new plan because we don's have that many rocks.

Here is the plan...the inner section is the deepest...

The plan.

Another grass to consider that I am loving: Pennisetum alopecuroides "Burgundy bunny." I wouldn't overthink it, grass is the curtain, your wildflowers are the color pops. We also like Panicum virgatum, although it is boring in the spring and summer. Another plant I love is goat's beard, very structural. But anyway, once you get your plants, you can move them around to see what you like. I basically create little montages of some grasses and then some wildflowers, with an eye to how it will develop over the season. You don't have much for spring, some wild geraniums might be nice, we had good luck with Geranium maculatum. Virginia bluebells do pretty well too. Neither can bake in the sun but they can grow in sunny spots if it doesn't get too hot in the afternoons. You can tuck the geraniums and bluebells under and around the rocks for some shade if they are big enough. Think of your plantings as "drifts" flowing like water.