Vault Basic is supported in the cloud.

Historically Vault basic server was not supported in a cloud environment due to possible licensing issues,

Autodesk have posted this on 2/3/21

https://knowledge.autodesk.com/support/vault-products/learn-explore/caas/sfdcarticles/sfdcarticles/Is-Vault-Basic-supported-in-the-cloud.html

Vault Basic (Server) is supported to be installed in a virtualized environment such as AWS or Azure or any other server hosted cloud service.

For Vault Basic (Client) see Autodesks updated Virtual Installation Guidelines.