Hello and welcome to Binky Bunny! Thanks for adopting a bunny from a shelter.
Even though seeds and nuts are normally not to be given to rabbits, sometimes they are recommended as a way to give some extra fat or calories to rabbits who may need to gain weight. Hulled, plain sunflower seeds have one of the highest fat contents of foods that can be given to rabbits. Walnuts are even higher. You can read about foods and their fat content in Lucile Moore’s book, Rabbit Nutrition and Nutritional Healing. She disagrees that nuts, seeds and grains should never be given to rabbits and thinks that they are actually beneficial and can add valuable nutrients to a rabbit’s diet – in small amounts, and not if a rabbit is obese or has some medical condition that would contraindicate them. Although other rabbit “experts” think that nuts and seeds should never be given. You could ask your vet for his or her opinion on some higher fat nuts or foods and see what they think about it.
I did once give plain unshelled sunflower seeds to an elderly rabbit who was losing weight, with the approval of my vet. They didn’t help him to put on weight, but he was old and had health problems and probably nothing would have helped him to put on weight.
You can up the pellet amounts a little, but you need to be careful with that. Too many pellets can lead to GI issues and can cause a messy bottom. You could add in some other hays, and even add in small amounts of alfalfa hay on an occasional basis