That's a young adult pigeon / Rock Dove. There are definitely various signs of illness other than the limb paralysis. The operculum / cere is off-color, it should be white. The discoloration could be either from a physical cause or a respiratory infection (probably due to fungus or yeast.) The fecal portion of the droppings is a bit loose and formless, but not totally, so it is borderline diarrhea. The clear fluid urine doesn't seem to be discolored, but there is a bit more than is normal, though not a lot or perhaps it only looks that way because the pad material is absorbing it well. The urates / solid urine should be white to just slightly off-white, and in the picture they appear to be a bit too yellow. That could be influenced by B vitamins in the supplement which is fine, or it could be due to an infection affecting the liver -- of which there are many different causes, bacteria / virus / fungus. The paralysis can also be a symptom of various infectious illnesses, or of physical trauma.
In short, the bird is sick and may also have some injury. Did you notice any wounds or bone-breaks while massaging the bird?
Pigeons can and do recover from illness and illness-induced paralysis, but they may need assistance eating and drinking.
I'd start by giving the bird a bath in room-temperature water with boric acid added (at about one teaspoon per quart of water.) Boric acid is antiseptic, anti-fungal, and kills external parasites such as mites. I use a large mixing bowl half-full of bath water with boric acid. Use one hand to prevent the bird from flying away, or from submerging his head in the water. Use the other hand to pour handfuls of the water over the bird's body until he is thoroughly soaked. Be careful not to pour water over his eyes, or beak where the nostrils / nares are located.
For the inside of the bird, I'd feed him about two ounces (roughly three tablespoons) of food per day, across several feedings. Their diet is mostly grains, seeds, and legumes like peas and lentils. I'd forego commercial bird seed mixes and instead give the bird dry/raw seeds which are also naturally antibiotic such as peas, lentils, cumin seed, fennel. I'd also include a high-energy seed such as sunflower kernels (out-of-the-shell), and barley and oats (or plain rolled oats) for a broader variety of nutrients. The vitamins which you are already providing will cover the few nutritional needs that aren't fulfilled by the seeds. A bit of raw apple cider vinegar added to the drinking water every-other-day at most would also be helpful in fighting infections in the digestive and upper respiratory tracts. Try every-other day for the first week, and less frequently as his symptoms lessen.
The bird can fully recover with a bit of supportive care, possibly for more than a month.
