Q.Should I Put My Cherry “tree” In The Ground Or In A Larger Pot?
Tree is in quotes because it’s still quite short. I managed to get a cherry seed from a grocery store cherry to sprout after putting it in the fridge and forgetting about it for a few months (almost threw out the container too lol glad I checked.) Without really any care at all, except an occasional watering when it was just insanely hot out, it grew leaves. The leaves died, and started up again this year even though I just straight up ignored the tree. Right now I feel like there’s too much rain (yard flooded, rains a few times a day) to put it in the ground. Should I wait until late fall like the internet says? Should I just put it in a larger container for another year? If in a container, what kind of soil? If In the ground how much do I have to dig? It’s 20” tall in a 10” diameter pot that’s 7” deep

Certified GKH Gardening Expert
That soil does look very wet, and possibly infected.
Putting it in ground will be much better than overcaring for it in container. You will want to wait until Autumn, or better yet, Spring. That container is still quite large for such a young tree, so it has plenty of time to remain there until time to plant.
The most important thing will be to NOT overwater it. This will be the most common cause of death.
This article will help you for when it comes time to plant:
https://www.gardeningknowhow.com/edible/fruits/cherry/cherry-tree-care.htm