Why do you think so? If the data had previously been synced via Dropbox and is still there, then you also need to enable Dropbox synchronisation in the desktop Joplin app, and it should download all your notes from there. There is no need to create any additional, paid accounts.
The same is true for the mobile app. If it's a fresh installation, just enable Dropbox sync in the settings, then let it download the notes from there.