Vaultwarden does not support automatic sync with Bitwarden, at the moment I do not believe even then official Bitwarden deployment would allow for sync across multiple self-hosted instances or self-hosted sync to cloud.
Only way to have multiple self-hosted instances tied together would be through a shared backend database, though this is more of a high-availability setup.
If all you need is majority of items included in your vault though, the CLI program could be installed and a script written to “export” items from your main vault, and then another part of the script uses the CLI to clear your vault and then “import” to the backup vault occasionally. There may even be some scripts out there others have come up with for this exact task.
Another possible option, if needing attachments to be synced as well would be to use Portwarden to sync between the self-hosted Vaultwarden and official Bitwarden cloud instance as described above.