Not every case can just be fixed that easy but it will help just to try. Seen a lot of situations where drainage is an afterthought in residential construction, specifically gutter downspouts and especially when the house originally had a gravel drive that was paved at a later date. That normally makes a small dam across half the property.

If you can get water flowing out of there it will make desirable species easier to grow since weeds enjoy poor soils- compacted, poorly drained, low nutrients, etc.

Fixing that would be priority one.

Thinking out of the box you could also plant a water loving tree or shrub there like a red maple or a few red twig dogwoods or even a group of wax myrtles.

Like Stork mentioned below, anything you plant now is going to be at risk when it gets hot here in a couple months. But you could get something down to retain the soil you have and keep the weed pressure from being immense.

I don't think machine aerating will do anything for you other than turn that wet spot into a soupy mess. They are heavy machines. Certainly not a prerequisite for getting seed to take as there is already plenty of exposed soil. The seed only has to touch, it doesn't need to be buried.

Fescue is okay with shade. For deep shade (less than 4 hours of sun) you will want to step into a shade blend or prune up your trees to get the sun you need