Would a vernal pond (as either a retention basin or a infiltration basin) be a viable solution for this drainage issue?
I don't think that digging a pond will help

The water is where it's at and the soil is saturated like a wet sponge, removing dirt for clear open water, aka a pond, is just removing the dirt in the pond, it won't change the water level.

These days the construction of houses take lot drainage into consideration but that was not the case for your older house. It looks like the surrounding area tends to slope right to your house and the low spot is at the deepest water.

Other Ways to Deal With The Water

In the picture it looks like your yard slopes down hill to a forest. You need to get water to a place lower than where it is currently, and the forest, if lower than your lowest spot near the house, is a great place for it. You would need to slope downhill to it at least 1/4" per foot of length


Dig a channel and leave it open, maybe gently slope the sides to make it look good like a old small valley or depression
Dig a ditch and put in a drainage pipe and cover it up. Place a catch basin attached to the pipe low spot near the house
To deal with it one-off style each season, rent or buy a pump and collapsible hose and pump the water over to the forest