Circling is usually a sign of brain disease, specifically the area of the brain where the sense of balance is controlled, called the vestibular nucleus. It can be affected by ear infections
(so I would have your veterinarinan look deep into the ears
when he is asleep on Tuesday), irritation of the nerves in the area (which could be a consequence of his dental disease), a brain tumor, trauma, and sometimes cats get "idiopathic" vestibular disease, which is a catchall phrase for "we don't know what is causing it". Sometimes with the idiopathic disease, they just get better.
In a world where all diagnostic tests are free, we would do an MRI on him. In this real world where MRI is not readily available, and fairly expensive, you may not be interested in this level of testing.
If I were seeing him, I would do a complete blood panel on him (I am sure this has been done prior to his anesthesia on Tuesday) and if it is normal, I would have him on antibioitics for his mouth infecion (I am sure he already is on antibiotics) and see if the anti-inflammatory medication prednisone helps his symptoms at all. I would probably wait and start the pred. once he has had his dental, but if it is really bad, I might start it sooner. I know a lot of people don't like to hear about putting their cat on pred., but it does not have the side effects in cats that people get, and is very well tolerated by most cats. There is a good chance that having the mouth problems taken care of, and maybe some pred. will take care of this. If he does not improve, you have to be concerned about some permanent damage in the vestibular area, and a brain tumor goes higher on the list of possibilities.
I hope all this is related to th dental abscesses, and you have your happy kitty back soon. Rebecca