This is the most frustrating thing about "Serverless", the major vendors don't really let you just purchase a "database", they want you to buy a whole RDBMS and provision it on a VM. Azure does have support for individual databases, but they want you to sell a kidney to pay for it.
Just like [https://discuss.vultr.com/discussion/1910/cloud-functions-serverless-and-isolates]
. I would like Vultr to manage a pool of Postgresql servers (or have a business partner do so), and then including that as a service in the vultr admin panel.