His fins are what we often call "clamped", meaning he is holding them very close to his body. Bettas will do that if they are unwell or stressed (other species can do it too I think but it's more noticeable with bettas); I still believe it's toxin related. I'm very glad that you chose to get a bunch of new supplies for your betta, he'll absolutely love his new home!!!
I sent you some links via PM about cycling your new aquarium, but in the meantime I'd suggest keeping up with the extra water changes (make sure you dechlorinate the water each time you do a chage and re-acclimatize the fish to the water and chemistry if doing a 100% water change). His fins don't look rough, honestly, though it's hard to tell when they are clamped.
Not all bettas will flare all the time, though. Sometimes if they aren't feeling well they won't flare, or sometimes they'll only flare when
they're feeling unwell - it varies between fish.