Backyard grading and drainage

Hello,

Between my and my neighbors home there is drainage area. The soil in that area is very soft when wet. I believe its mostly clay soil. As I was walking through, a small spot along the canal gave in and I was able to push my foot really deep into the ground, I am not sure if there is anything under it. Maybe a weeping tile, but my understanding is that those are installed right near the foundation. I added 2 pictures. Any ideas about about what can I do to take care of it? Do I just cover it with soil ? Or do I have a drainage problem. If it is a drainage problem, what kind of services can can I contact to take care of the problem? My basement is not wet, but that area collects alot of water. If I was to creat a slope, the water will drain acrosd to the sidewalk.

Thank you