My research tells me that sore throats (pharyngitis) themselves without other symptoms are uncommon in cats. If a cat has a sore throat it may be that they have a viral illness or poor oral health and a mouth infection. They may have a foreign body stuck in their throat which results in symptoms much like that of a sore throat.
An alternative possibility is tonsillitis which is also rare in cats. As for humans, they can become infected and inflamed. The symptoms are like those of a sore throat. The cat may have a fever. Most cases of tonsillitis are caused by bacterial infections.
Anecdotally, a cat may develop laryngitis with results in a silent meow. However, perfectly healthy cats can develop a silent meow or they may have it all their lives. It can be a personality trait. I wouldn’t automatically equate a silent meow with a health problem concerning the cat’s throat.
Foreign bodies in the throat of especially kittens are not that uncommon. The cat might gag and extend their neck on swallowing. They may choke on swallowing.
The signs of a sore throat or fever, coughing, gagging, vomiting and pain in the throat when swallowing resulting in a loss of appetite. A veterinarian will examine for diseases causing sore throats. Cats with sore throat should be on a soft, wet food diet diluted with water or a plain broth at a liquid consistency. Antibiotics are administered and pain medications may also be required.