I have the same thing, runny nose while eating or afterwards. It is not related to Long COVID since I’ve had it a long time. (I also have other nasal issues due to allergies…post nasal drip, coughing, etc) the runny nose while eating is caused by nerves in your sinuses being too close to the surface.

Have you discussed the Clarifix procedure with your doctor to see if in your case it would be helpful? I actually have this procedure tomorrow at Mayo ENT. (I’m hoping it may also help my post nasal drip). Google the procedure; it works by the doctor freezing the area of the nerves inside your sinus cavity. It may be worth exploring. Best of luck!