UPDATE with question.
So, you know how I said he was fine? Well... remember I had said he was on meds and looked worse? Then I did a water change, I had added salt that time and then the next morning he was like a brand new fish so decided he was fine. He continued being just fine. So, I did a water change 5 days later (I think) with just the regular water and dechlorinator... and he went back to being all lethargic! I puzzled over it and last night dissolved the salt and added it to his tank again and....... this morning he is 100% again!! Fully happy, enthusiastic, curious, etc etc.
So... the question is... why is salt making a difference? I live in the UK and the water is hard enough on its own, so it can't be that as it was said bettas prefer softer. Is the salt actually treating something right now and I just don't know what?? That bit of black on his fin from the photo is unchanged, neither worse nor better.