I'm currently doing the opposite (migrating data from non-Cloudron to Cloudron environment) but I assume it's similar in ways @girish described so just wanted to mention some caveats for people trying this:
It's not possible (or at least not trivially possible) to migrate your users. The Vaultwarden docker image uses sqlite while Cloudron uses mysql. The org that I'm trying to migrate has less than 30 users so I'm ok with having to re-invite everyone to the new instance. But if you're trying to migrate a bigger Vaultwarden installation, you'll either have to figure out how to transfer the users between mysql and the sqlite database, or everyone has to create a new account.
File attachments have to be copied manually. You can't just scp the attachments folder from one server to the other, this means every attachment has to be downloaded manually through the gui and then uploaded again to the new instance.
Exporting and importing the vault itself was a matter of exporting a json file and then importing it in the new vault. Took less than 5 min.