Advice for shady dirt area under trees (drainage + moss problem)

looking for advice on what to do with a problem area in my yard. The area is very shady, has drainage issues, and grass won’t grow there. Right now it’s mostly dirt patches with moss. When it rains, water tends to sit there, and it just looks messy overall.

I don’t have much money to spend, so I’m hoping for budget-friendly ideas or DIY solutions. I’m open to anything that would make it look cleaner and more intentional — mulch, ground cover, drainage ideas, etc.

If you’ve dealt with something similar under trees, what worked for you?

Thanks in advance!