There are a lot of incorrect statements here.
Synchronization in the Joplin Android app functions to align the backup data storage paths, such as Dropbox, device folders, or other cloud storage services.
No, it is for syncing your data only. Backups are performed by the the backup plugin, not by syncing your data.
However, to access or recover notes that have been deleted or that you want to access from different devices, users indeed need to access their Joplin account through a browser or use the desktop version.
Additionally, to access data that has been synchronized to Dropbox or other storage services, a paid Joplin account is required,
Joplin Cloud is the only "Joplin account" and the only sync target that payment is needed for. None of the other sync targets (Dropbox, WebDAV, NextCloud, S3, Local file system, Joplin Server, OneDrive etc.) would require a paid account and none of them would require a browser.
Joplin is, and always has been, offline first. If you lost your local copy of the data then you need to, as people have already suggested, add your sync target to download your data locally again to bring it in sync once more..
the Joplin app on Android does not support full management of notes synchronized from cloud storage like Dropbox directly
Yes it does? You sync your client to get the latest data then any changes you make are pushed back to the target just like any other client. Any changes in the target are routinely synced to your local copy whilst the app is open.
Evernote is smiling in the corner, knowing its position remains unshaken!
You mean dying in the corner haemorrhaging users?