Orthanc comes with an SQLite database out of its box. SQLite does have performance limitations, though.
Among the additional storage plugins that have been created for Orthanc, there's one for PostgreSQL that will enable cloud-based storage and handling.
Osimis ensures compliant cloud storage thanks to its DICOM split feature that operates a state of the art de-identification process to store PHI data and pixel data in a segregated and encrypted fashion, all in ISO27001 and local data privacy regulations compliant cloud servers.
This plugin furthermore covers the needs for a fully fledged SaaS application. In combination with all the other Orthanc features and the zero footprint DICOM viewer plugin, one can start running all sorts of DICOM-based applications in the cloud.