If you still have the parent items in your library - just without their original attachment - and when you try to open it, Zotero says it cannot find that known attachment file, then the Attachment Scanner plugin can identify and tag those items with missing attachments (#broken). But it is then up to you to fix them, eg by pointing each Zotero "can't find" dialog to the file.
https://github.com/SciImage/zotero-attachment-scanner

But since you say "My hypothesis is that they're not listed in zotero.sqlite" (where attachment locations are recorded), that suggests that the parent item might *not* have any attachment recorded at all. The Attachment Scanner can also tag items with no recorded attachment (#nosource).

If the files in question under Zotero\storage have *no* parent item (nor exist as standalone PDF entries in Zotero), that's a harder problem. Because by definition Zotero has no knowledge of the item or such "orphaned" attachments. To help find the orphaned files, you would need to generate a list in your OS of all PDFs (and any other attachment file types) under Zotero\storage, and then compare that list to a list of all known Zotero attachments. The latter list can be generated as described here:
https://forums.zotero.org/discussion/comment/440946/#Comment_440946

If you know the 8-char folder name where a PDF is located, you can check if Zotero has any knowledge of that location by entering the folder name in quick search for "All Fields & Tags".

Other suggestions to fix your problem might be more obvious if we knew *how* your library lost knowledge of some of its stored attachments.