Before proceeding, I would have your neighbor have a septic guy come out and mark the system. His leech field should not be on your property, and I see a lot of trees back there that are far more likely to be the problem.

Since it is already shady, a shade structure doesn't make sense, but if you like to watch the rain, a roofed rain structure might? Kind of a remote porch.

Or to replace the veggie garden, you could install a small potager garden with raised beds. You could grow herbs (many of which are shade tolerant) as well as edible flowers and leafy greens, which can tolerate shade as well. Or skip the edibles altogether and just plant begonias, impatiens and other shade-loving flowers. A water feature in the middle could work, maybe with some turtle-safe greenery so they can get a snack. And of course a place for you to sit and enjoy it!