Sorry to hear your little guy is not doing well. I LOVE betta, have kept them for almost three decades. I have recently fallen in love with corydora also. I have many of both. They make great tank mates, depending on the betta personality. Some love company. Others won’t tolerate it. If you want to go a medication route, I would say try Aquarium Co-op Med Trio, following Cory’s treatment amounts. If he is not lethargic and is eating well, don’t panic. I have had betta tails change appearance with age. Crown tails have similar tails, but are heathy. Do fin ends look solid or frayed? Are they just whispy looking or actually torn. You may want to continue with salt but also add almond leaves or untreated drift wood. It will darken the water, but I have had it be nothing but extremely beneficial for bettas. Tannins contain natural antimicrobial qualities and present a more natural environment for betta. Best of luck to you both! And you are right about this tank mate match up. In my mixed tanks, the betta don’t eat from the top anymore. They think they are corydora, eating and swimming with them. It is adorable.