With the water that muddy, the only way to know the depth is to go out on the water and test depth with a rope/string and a weight.
You may be able to call up some historical satellite maps and see what the pond was like over the years. Might give you some peace of mind.
I was looking while you were typing.
I've found the pond in multiple satellite apps including google earth, maps, zoom earth, etc.
Looks like it's there in every picture, with some having no construction anywhere near the site. In every view, it's got lots of water.
So, I'm not sure what this means to me, but perhaps it means that a well placed burm, except for where the overflow would exist into the flood easement at the back of the property to allow overflow to head into that pathway, and some planning to clear up the water, etc., this could work out well?