See the 4th bullet point here: https://www.zotero.org/support/pdf_reader_preview#additional_info

It doesn’t sound like you really read that section.

I mean, it's literally not a lock-in problem. That's the entire point of that section.

As it says, you'll always be able to take your annotations and move them out of Zotero, but we can't provide the experience we want to provide with annotations stored in the file. Storing annotations in the Zotero database is necessary for all sorts of functionality, now and in the future, that will make Zotero's PDF reader different from every other PDF reader out there.

From my understanding I can export the PDF with annotations and then would have to re-add that PDF to zotero to get to the desired state, which sounds really cumbersome.

We've said that it may be possible in a future version to do a one-way transfer of annotations between the Zotero DB and the PDF file (or vice versa), deleting the source annotations. What we can't do reliably is have annotations stored both in the Zotero DB and also in the PDF, with the possibility of external edits at any time — doing so would be error-prone and risk duplicates and conflicts.

@dariokaji: It sounds like you still may be misunderstanding this. It's not that you can "take the notes" out of Zotero. You can export PDFs with your highlights and notes embedded in the file as standard PDF annotations, whenever you want to. It's just that, while you're using Zotero, there are major benefits to having the annotations stored in the Zotero database. If you want to continue using external PDF readers while using Zotero for other reasons, that's fine, but data portability is absolutely not a reason to do so.

@dstillman yes, you are right, it is possible to export a PDF file containing the Zotero notes. I also understand that there may be reasons that justify Zotero keeping the notes separate. However, the ideal is that this incorporation of annotations into the PDF would occur automatically, without having to export each annotation made in the file. I think the possibility of having a Zotero Mobile is a big step forward, and I also recognize the speed with which the application is working. I just commented as a reflection for future improvements.
@adamsmith it is an excellent observation. It is possible that this will happen in the future.

(not sure if that's just a typo, but you wouldn't need to export 1 by 1 -- you can export them all in one step)

@dstillman wrote, "We've said that it may be possible in a future version to do a one-way transfer of annotations between the Zotero DB and the PDF file (or vice versa), deleting the source annotations. What we can't do reliably is have annotations stored both in the Zotero DB and also in the PDF, with the possibility of external edits at any time — doing so would be error-prone and risk duplicates and conflicts."

I understand the concern about conflicts. I just got the PDF reader working and tried it. It appears to me that when I open a PDF with externally made annotations, that Zotero reads the annotations from the PDF and writes them to the Zotero DB.

If this is the case, I don't understand the problem with making a setting to allow users to automatically write their annotations to the PDF every time they close the Zotero PDF reader tab. Couldn't it work like this: Zotero has annotations in its DB for a PDF. If the user has added some annotations externally, Zotero doesn't know about them, but that's not a big deal for the moment. User opens the PDF with new annotations. Zotero wipes the existing PDF annotations it has stored in the database (every time it opens a PDF, without checking for any changes) and overwrites them with the annotations stored in the PDF. It would be a performance hit, but it doesn't seem to take long to scan most PDFs, and for some people, being able to reliably read and add annotations to PDFs from outside Zotero would definitely be worth it.