That is one tough fish and pretty, poor guy, but now his life will be better.
Yes, warm clean water, frequent pwc and maybe some StressCoat, it has Aloe.
You may want to look into using Epsom Salts to help heal them. I have used it before and had good results. It needs to be pure magnesium sulfate, no additives.
And one OR the other, if not going with the
Epsom salts, I might use some aquarium salt. 1/4-1/2 tsp per gallon would be fine for aquarium salt. Just keep it in the same concentration for awhile, for pwc and as it seems to be cleared up and healing you can go to a lower amount and reduce again the next pwc and reduce then end with regular treated water.
These would be best mixed into liquid concentrate with tank water (like after a pwc "clean" kind of tank water) or freshly treated water, and added gradually over the course of 2-3 days. Divided into portions and added maybe 3 times or 4 times over 2 days if you are going with a medium concentration.
He can grow back his fins nicely.
Congrats on the new additions!