Waterproofing plumbing stack in bathroom
What does waterproof the pluming mean?
Plumbing is designed to keep the water    on the inside of pipes.
If there is a leak in a pipe then the pipe should be repaired.

He was also unsure he was allowed to waterproof inside the stack. Is
this correct?

We can  not say what the plumber can or can not do.
Waterproofing the inside of pipes is not  normally done unless it is an underground or otherwise  an inaccessible pipe. In that situation there is a  procedure, internal pipe coating, to coat the inside of pipe instead of digging it up.

And are there any issues with waterproofing my floor?

If the pipes are not leaking then waterproofing the floor is not necessary, If the pipes are  leaking then waterproofing the floor is not the correct coarse of action.