Something native would be awesome and beneficial, they have deeper roots that help with the excess moisture.
Golden Groundsel (Packera obovata) is pretty aggressive and hardy. Not sure how wet your conditions are compared to what they like. For reference we put it in the south facing yard (clay soil) as ground cover around some shrubs (some shade) and we are happy with it. One of the first things to be green thru winter. Looks particularly nice in masses, especially when in bloom. and of course it's good for pollinators. I'd estimate that the plugs grew 4X in size since we put them in a year ago, not sure, one of the fast growing plants for us that we have put in so far.
I bought ours at prairie nursery. I'm not allowed to post links as a new poster, but if you go to the website, you can use their search bar to find it. They also have a list of other groundcovers you can check out.
Though they don't have Golden Groundsel, Agrecol nursery in wisconsin is another good seller. I recommend taking a look. They sell reasonable price plugs trays or even mats with seeds sowed in. I've bought from them a few years in a row and emailed and called a few times for quick answers to questions.
Again, I can't post the link but they come up easy in a search.
Depending on how much room you have and ground to cover, possibly could also think about adding some under story shrubs like dogwood shrubs. Red twig dogwood can be nice.