The doctors wore plague masks for a reason - the "beak" was stuffed with all sorts of herbs that were believed to ward off the plague. At least the doctor's respiratory tract was protected and he breathed air that smelled more of all sorts of herbs than ulcers of patients and corpses.
The plague took a robust walk across Europe and at one time nearly killed Venice as a city-state. Therefore, the emergence of Venetian masks, with a beak-like nose, as terrible masks, designed to cause horror - was predictable. But apart from everything else, the beak of the mask also has a utilitarian function - since it does not prevent the wearer from drinking even from sufficiently large glasses.
It's clear about the functionality, but symbolism? It is symbolism that interests me, and not what was put into the "beak" and for what purpose.
I found two theories without much reinforcement.
One each: the masks symbolized a certain Egyptian deity, which should have scared off the disease. Which is not specifically indicated. I googled, in appearance, Thoth is most suitable. But he was revered for wisdom and knowledge, it does not seem that this is our man. Upd. the Internet says that he taught people medicine too. But what does the ancient Egyptian deity have to do with the clergy and all the affairs?
According to another theory: it was believed that the infection is transmitted by birds and the doctor symbolically takes over the disease, since it looks like a bird. But this also looks incredibly tense, because the main reason was considered to be miasms, in fact, the mask was created to fight them.
Why did the Frenchman Charles de Lorme create a mask in the form of a bird's head?