What to do about sneezing cat with infected (?) perforated sinus

My (male 9 yr) cat keeps sneezing due to a perforated sinus following a tooth extraction in 2019. The vet said back then he would keep sneezing with his left nostril. He sneezes especially after eating and also has greenish slimy eye boogers on the left. (Before extraction he sneezed worse and had a foul breath).

But, antibiotics after a later dental treatment did reduce symptoms temporarily, so there’s an infection. Now another vet (a substitute) suggest rhinoscopy to see what’s wrong. My own vet agrees while previously saying they probably won’t find anything.

1. Is rhinoscopy a good idea? 2. How much does an infected (?) perforated sinus bother him? He seems to feel fine (antibiotics don’t affect his mood like that extraction, he was soo happy). 3. Is there a way to stop the recurring infections?