the photas are very helpful. and he sure is handsome

i do NOT think this is finrot. the spaces between the rays are too even. what i suppose is happening is that the rays are growing faster than the filaments between which causes the "gaps" you are seeing. black edging isnt always bad. some bettas (depending on color) have darker margins to their fins. to me it looks like natural coloration. i swear i can see clearish bits between the rays-the filaments are growing to fill in the "gaps" between the rays.
have you noticed any actual fin LOSS? or just the new pattern of growth? depending on his age, he may just be going through a "growth spurt" in the fin department

i had a very wee boy who was given to me as a standard delta..about 4-5 month old i noticed almost what you are seeing (scalloped edging to his fins)and kept his water VERY clean and kept an eye on it(no meds). well, as it turns out, he grew into a beautiful OHM rosetail! they can change very drastically very quickly when juvies-especially with good environment and good food.
my suggestion-keep water top notch and watch for signs of actual erosion. if youve already positive that he is actually losing fins by all means continue meds. if not, id stop with the meds and just wait to see how he morphs. i wouldnt worry too much about the dark margins until you notice actual loss. as stated, some bettas have a dark edge to their fins when fully mature(and based on his coloration i wouldnt be surprised if this is the case with your particular fish)

he really is lovely!
hope that helps a bit.
cheers!!