While not Microsoft offerings, there are some options available: my company Aiven (https://aiven.io/postgresql https://aiven.io/postgresql) offers managed Postg

While not Microsoft offerings, there are some options available: my company Aiven (https://aiven.io/postgresql https://aiven.io/postgresql) offers managed PostgreSQL service on Azure as well. ElephantSQL (https://www.elephantsql.com/ https://www.elephantsql.com/) is an another provider with hosted Postgres on Azure.