I agree you shouldn’t need to bring in soil to do this if you want.
I have had good luck micro swales, puddle swales, crescent swales, whatever you want to call them. Basically dig out a small puddle size hole and mound the dirt into a planting mound. It is great for those trees that hate wet feet, but not a ton of work even by hand. Try not to take ALL the topsoil from the puddle area if you want to replant it, fill it with organic matter if you go all the way to subsoil—wood chips, hay, straw, grass clippings, cheapest easiest you can get.
Keyline plowing or subsoiling can help with drainage if the issue is a compaction layer/plow pan, but won’t help much if you have deep clay.