(Zone 7a VA)

Help!

This is the East side of my house, and an area that we never really use because there is not much there. It is pretty heavily shaded once all the trees sprout their leaves. Tree in the picture is a large southern magnolia (which is healthy), and also our neighbor has a sweetgum that is not too far. I want to plant a shade garden here this spring, but today after a night of rain, I noticed this big rain puddle that is up to a few inches deep.

I never noticed this much before, but probably because we just don't go there often especially right after the rain....

Is there something we can do to improve the drainage in this area, such as amending the soil? Or would it need bigger project such as french drain, etc?

There is a drain further down (i.e., behind my back when I was taking this picture) alongside the fence that previous owners put in but not sure how effective that is. Part of that is broken as well..... I assume nothing really will grow well here (currently it is grass/weed patch), and we want to do something.

I would appreciate any opinions!