I've trimmed 1 whole plant and about 1/3 of that plant but haven't seen anything else like it. I was hoping it was gooey strands of resin. I was scared it was spider mites.I would say it's either well-established spider mite infestation or a form of fungus, but I don't see any of the darkening that would typically accompany bud rot.
Could also be a random spider web, if there's no other evidence of spider mites. If I was a spider looking for a buffet, I'd hang out where bugs like to travel, and that would include some types of plants.
If it were only a strand or 2, I'd say to check to see if your dog is shedding.