The solution proposed by stefan here could align to how I use notes in zotero.
I use notes attached to papers to remind myself what the paper is doing there, or to provide some searchable terms more relevent and so more memorable to me. For instance, I often have notes attached to paper saying things along the lines of "First paper to use drug x in fish, although they use a slightly odd dilution scheme. Provides rational for my dosage @ 0.5mM".
The paper may be on a subject utterly irrelevant to drug x, and in fact the drug x info might be buried somewhere in a supplemental figure or might only be a passing comment in the methods. So, PDF annotation isn't the important factor and is a bit of a cludgy way of doing it. It's a little more involved than a tag, but less involved than annotation.
Much better (for me) to have a virtual post it right on the "cover" of the paper which is searchable for the once in a blue moon occasion I provide the paper to a student to read, or to a colleague who wants to know why I used drug x at concentration y.Then I can just push the PDF to them directly without having to faff with an annotation interface.
I also find the notes useful for chaining together papers following a particular topic I'm interested in or point I want to prove / disprove. Again, the papers may be on different subjects, and so are within different folders to start with. Even if I have organised them into one folder on the particular subject I'm following, it's very useful for me to have a top level note associated with each paper along the lines of "This paper started the whole idea of xyz off. But the experements here don't really addres abc. For that see (other paper). Maybe they didn't see fgh so didn't bother". Then paper 2 would have a similar note associated with it.
Again, this scenario isn't really tractable to being condensed into a tag. And although it might be possible to have the papers in a folder together, it's still really useful for me to be able to see exactly what's going on with the papers in that folder using just the notes and really, really helps me in keeping my brain on track! The less I have to dive into the paper itself the better as I will just then tend to get distracted with what else the paper says, or the other papers referenced within.