Sync is not a backup. As you might have just learned, If your db gets corrupted locally, the error will be propagated to the sync target.
So, if you notes have some value to you, you must have a backup regardless of the sync target (even if it's filesystem).
Here's a link to the plugin making automated backups
You mean you synced a clean instance of Joplin to Dropbox and it only downloaded one notebook?
Or you downloaded the folder from Dropbox and tried import it manually after which the import shows up as one notebook?
Do you have any notes without a notebook? Search -notebook:* in Joplin and see if it returns anything
I cannot know if your database is corrupt or not. The best I can do is to give you a hand in navigating the situation. There's a possibility you're having completely fine database that just need an import. Or the database is corrupt and you can only extract useless bits and pieces of your notes. To see which is it you need to try restoring deleted notes (as described in the post linked below) after the attempt of sync is complete
However, this is the last resort method, so before that we gotta make sure there's no other device having noncorrupted data.
I'm assuming you don't have any other device with your notes, is that correct?