If you were going to invest in the property, I would suggest raised beds would help greatly. Otherwise, why not do large container/tub plantings--then, you could take them with you. Can't think of any annuals or perennials that tolerate being submerged like that. You are not alone, millions of us this year are either dealing with severe drought (West) or depressingly unrelently, torrential rains.

There are some native plants that would work for you in that situation.

Any of the cultivars of the Panicum Grasses, "Switch Grass" would do very well, they can take standing water, clay soil with poor drainage and drought periods. There are many cultivars that are very pretty. My favorite is 'Northwind' which is so vertical it looks ironed and a sort of deep olive green color. Looking at your picture, the vertical aspect would work in that kind of narrow space by the sidewalk the best. Another fairly vertical one is 'Heavy Metal' which is powder blue and there are some that turn red in fall as well. These get around waist or sometimes chest high not counting the blooms and the clumps get larger and prettier every year. They are very popular in the nursery trade and easy to find all different kinds of cultivars because native grass gardens are sort of an in thing currently. Some other low growing types of ornamental grass would be worth a try I think because they can be pretty forgiving.

Physostegia, Spring Obedient Plant will take poor drainage and standing water.

Hibiscus militaris, Halbert Leaf Hibiscus grows in freshwater marshes or shallow water and will also take poor drainage. It gets 3 to 8' tall

Maximillian sunflower grows wild in ditches around here in slimy clay that later dries out hard as bricks so I know these would do well also but you'd want to plant something at the base which can get ratty looking toward the bottom part. It gets tall like a hollyhock, blooms in fall.

Wild Ageratum "Blue Mist Flower" is another.

Otherwise, you will have to build up higher. We did that in some areas with a couple of large loads of topsoil and sand and it solved the problem.

Maybe build a small levee or floodwall to direct the water away from the yard.

Blueberries, huckleberries, seviceberry, dahoon holly, winterberry holly, cyrilla, tupelo, cypress, red maple, sourwood and stawberries could be some options.

Not sure it helps but some places do not allow homes to be built lower than the crown of the road.