If your library is out of sync on the desktop app, it is likely that your database needs to be rebuilt. This is a simple process that should only take a few minutes.
To do this, launch the desktop app and navigate to the main menu of the app and select "sign out"
Once you select "sign out", select "delete local data":
Please note this will not delete any PDFs, annotations, or other content from your library; it will only remove the background database of your library on the desktop app, which will then rebuild once you relaunch the app. When you first log back in after selecting "delete local data", a sync will begin which will take anywhere from a few seconds up to 15 minutes, depending on the size of your library.
Once this sync is done, your library should be up to date.