Tooth roots tend to be behind a teary eye (when tooth problems are involved). If it is milky though, that sounds like a possible infection. Does he have any other symptoms?

Yes.

You can probably wait until Monday. If he is eating/pooping/etc. then it isn’t an emergency, in my opinion. The problem with tooth root problems is that there is constant irritation in the sinuses and/or tear ducts. Wooly is “stuffy” all the time. Sometimes, bacteria will start to multiply in his sinuses. I can tell the difference between him being his normal sneezy self and not feeling well. When that happens, he needs some antibiotics to get it under control again. Sometimes it causes a problem in his tear duct and, now, his ear.

What sort of surgery is the vet wanting to do?

I suggest having your vet do pre-anaesthetic bloodwork to make sure he is healthy enough to undergo the procedure.

My Bindi has chronic blocked tear ducts that my vet flushes regularly. When they get really blocked up the secretions are often a sort of clear/whitish colour and sticky.

The vet can buy nasolacimal stents to drain the tears during healing. They keep the duct open long enough for the tooth to heal. It would have to be cut to length for rabbits.

The company I work for sells them. They have a rim at the top so removal after use is easy.