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I don't know about your motivation to move to self hosted but keep in mind that self hosted not only means to move your directus instance to a private vps. You also have to consider how to harden your vps against attacks. Also you need to consider how to do backups. That may not apply for you, because your project will not contain important data. But keep that in mind before paying someone just for the migration to a vps of your choice.
All these aspects are included in the cloud version and in services like elest.ioand restack.io.
Maybe there are some more services like that. Just Google "managed directus".
I could help you with migrating and basic hardening of the vps including automatic backups to S3 or webdav. But this will for sure cost a bit more than other offers.
FYI I work with coolify as server/docker overview tool
sacred jay