I watched the video of your pigeon carefully I would not say he is slow. Feral pigeons have to compete for food, fight for food, so they are constantly in turbo mode. Pet pigeons have their food, water and shelter secured so they are relaxed, sleep a lot more, and just look for ways to be cozy. Also please note that birds that are not flying every day will have much less muscle mass on their chest. When you palpate the breast bone, bone that goes along the whole front of the pigeon, you should feel muscles on both sides that are sloping gently from the tip of the breast bone towards wings. In captive pigeons that don't fly a lot these muscles can even be a bit lower than the tip of the breast bone. What you don't want is very small muscles so that the breast bone sticks out and you can feel its prominent ridge that you can basically grab with your fingers on both side - this is toot hin, and you also don't want muscles to fill out so they stick over the breast bone - that is too fat. So as long as you are in between, you are good.
If your pigeon is indeed thin, the best thing to do is bring poop to a vet to take a look at it under the microscope. It might happen that the pigeon has internal parasites, maybe he has a fungal infection in its crop or guts, or some mild bacterial infection that in interfering with digestion. Maybe there are issues with his liver or kidneys.
Lastly for food I prefer to feed a complete seed mix to my pet pigeon, from which I remove sunflower seeds and avoid any mix with hemp seeds. This is because I know he digests poorly fats. In addition to seed mix I also give grit (granite rocks, crushed shells and redstone), mineral block for pigeons (contains all minerals and microelements), and I also give in the morning seed mix that is coated with vitamins. Especially for indoor birds you should always provide supplements - both vitamins and minerals.
I suppose pellets are the best way to go as you secure all the nutrients at once but for my pigeon he was not doing so well with pellets as they were just too nutrient rich for his mostly sedentary life and some liver issues. he also had oily, brown or even smelly poops on pellets. So you can try to transition to a seed mix and suplementation and experiment a bit. I also noticed that fresh vegetables, even thou they are good for birds, my pigeon does not digest all that well, so I offer him but let him choose if he wants to eat them - I never mix them in to food to force him to eat them. Sometimes my pigeon will eat a whole kale leaf, and some days he will not go near it. I am confident birds to know what they need and it is best to provide variety of healthy foods and let them choose. The less healthy foods that should be taken in small amounts - sunflover, hemp, peanuts, niger seed, flax seed, sesame seed (all rich an oily) I give in small amounts as a treat.