Try large ferns, like Cinnamon fern or Siberian or Louisiana iris.

Two things. First, get a soil test done. Your local Horticultural Extension office should be able to do this. Then when you get the report, amend as necessary.

Second, divert that water coming out of the downspout. Bury the downspouts if possible, and take them about 20-feet from the house. Just do something with that water, because if roof water is flowing onto the lawn that close to the house, it could lead to foundation problems or a flooded basement, if you have a basement.

Wet areas near homes are bad, bad news. They cannot be resolved with plantings. You must divert the water. The best thing we ever did when we moved to this house was get 13 downspouts buried. I know this because six weeks ago when one of the popup drains in the yard, the one that spills out the most roof water, clogged before a torrential rain. We got 5" in two hours, and wow, did we ever get water in the basement. The sump pump just couldn't keep up.

After that, then you can decide what to plant.