Generally the recommendations are that a rabbit’s diet should be about 85-90% hay, 10% veg, 5% pellets.
While I also only feed my bunnies a spoonful of pellets, they are important for nutrients and vitamins. To ensure they’re getting the correct nutrients without pellets, you need to feed a huge variety of greens each day (I believe 8 to 10 different types), which isn’t practical for most of us. A small amount of a hay-based pellet won’t do any harm for most bunnies.
I give my dwarf rabbits roughly a handful of veg twice a day, (normally a variety of 3/4 types a day). I feed them various lettuces, rocket, dill, parsley, mint, coriander, kale, celery, broccoli, cauliflower, spring greens, spinach, watercress. For occasional treats, they get blueberries, strawberries or banana slices.
As with any new food, you should increase gradually, so don’t go straight from a teaspoon to a handful, and give very small portions of anything entirely new.