The house may have had a trash burning area in the bad patch. 130 years is a long time to accumulate things. I suggest making a measured plan of the yard to start with. Indicate the puddle size and depth. If you have an overhead view from google streetview or a plan from your escrow papers, both would be good ways to start with the outline. Are there drone photos from the listing?

Another thing you as an urban archeologist could do is dig a couple more holes in random parts of the problem area to see more of how far down the junk goes. A foot or two deep may be helpful. Wear sturdy gloves. Spark plugs, broken bottles and old cans are a tip off that it was a trash burning area.

Professional landscapers have access to power equipment that will fit through typical gates.

Do you have a photo from the back gate showing the full yard?

thank you for the suggestion! No drone photos from the listing. Here are some photos of the length of the back yard, shot from the house. The patches in the back are being solarized, just FYI. Blue thing is a shed, red thing is a chicken coop. There are drainage issues throughout the yard, but the area in front of the shed is the one I'm discussing here.

I think I can explain the ‘inexplicable’. Judging by the other self sown weeds in the area I don’t think the blackberries are a deliberate planting. I imagine they’re the result of birds sitting in the trees above. Same goes for the straggly grape and the Virginia creeper. There are even some grape seedlings visible. I can’t see any cultivated plants in the bed at all.

Thanks for photos. It looks like you have already done a lot of work.

If you have trash pickup that will accept a few rocks and broken tiles every week, you could try the slow-but-sure-and-free method of collecting (say) 20 pounds every trash pickup day. Since it's already late August, you could cut the miscellaneous weeds to the ground now, then nip off any new sprouts until first frost discourages new growth.

Next time it rains, take photos of the puddles. These photos will be very useful when talking to a professional landscaper.

You didn't ask, but here's another comment. In terms of immediate improvement in appearance from the house, when you have time you could move the hinges on the big shed doors to improve the way they close (the screw holes may not be holding any more), then use any leftover blue paint to match the gate to the house.

A fun thing to do is use a pressure washer on old sidewalks and bricks. Consider relaying the old patio bricks in front of the shed doors to avoid mud splashes. You're in an area where frost heaving may be important, so another solution may be more effective.

@mad_gallica (z5 Eastern NY) our current working theory is that they built up the hill using clean fill and it *used* to have a soil cover on it, which has since eroded (possibly due to drainage issues caused by the improperly set patio above). One possibility would be somehow recovering the area (and maybe replacing the retaining wall)