Single-mode, multi-mode, etc. All fibers. Let's use my LASER marker at work as an example. Divergence in that fiber happens AFTER two things happen - first the photons need to leave the fiber,then they have to cross-over their 'hip' (where the collimated beam is tightest) THEN they diverge.

That's how fiber LASER markers work. I'm the operator of them where I work (I do everything outside of SMT - x-rays, LASER marking, high-voltage testing, etc.) Every LASER coming out of that fiber hits focal point about 2 feet past the fiber, where it begins to diverge.

Do not trust a LASER coming out of a fiber to be unfocused or not have enough power density to blind you. Period.

That's fine safety guidance but on the facts this is not correct.

For single and multimode fibers if it has a smaller focal spot some distance the fiber than at its tip you are talking about an assembly that includes the fiber plus an optic.

This is unambiguously true for single mode fibers. Multi mode one will diverge less

I could see there being some exception for a strange fiber which has a multi-emitter output, was nanostructured, tapered, etc..

"For single and multimode fibers if it has a smaller focal spot some distance the fiber than at its tip you are talking about an assembly that includes the fiber plus an optic."

A properly-shaped and polished fiber tip is already the optic. That's literally how it's fed into the galvo in a fiber-marking LASER. I'm also responsible for the maintenance on all equipment in the facility so I've had those machines apart more than once.