I had the exact same problem with clamped fins and this is how my betta looked (picture below taken by me when I first saw it like that)
First of all, a larger tank is not the solution. My betta lives in a 1 gallon fish bowl and he is happy, active and healthy. My problem occurred when I left the windows open for too long and the room cooled too much along with the water... I treated my betta by doing 50% water change every day and 100% water change every third day. I bought Dajana Aloe Gel which helps with relaxation and injuries. I also put a pinch of kitchen salt whenever I did a water change (yes, kitchen salt, not aquarium salt, some people say that it is bad because of the Iodine but an amount that small is really ok and good if you can not acquire AQ salt as it helps with fin regeneration). The treatment lasted for 10 days and on the 10th day he looked brand new and he was swimming, flaring at a mirror, eating well and generally very happy. Make sure to pick up any leftover food and keep his water clean and warm enough. This isn't fatal, I believe he just got a cold. Try feeding him live food which can be bought at a pet store or caught in your own room (small spiders, mosquitoes, etc.). Every betta is different so I can not guarantee that the treatment I did will work for you too. Also, from what I've seen on your video, you should really create a more joyful surrounding by putting some colorful rocks or marbles and a fake plant. I wish you and your betta all the best!