You are frustrated.
You can drag and drop PDFs to the iTunes Library icon (iTunes open). They get organized into the Books section. They seem to sync to your iPhone (iPad). Except they don't. Nothing shows up.
You've tried everything. Maybe even inspected permissions.
See that lovely little button that says "Books"?
Now you see your PDFs.
You are welcome.
PS. You can create a collection called "All" and, using Edit, tap on items, then tap Move you can put your Books and PDFs together.