Ability to store the prefect database to a custom PostgreSQL schema

[francbartoli]

Describe the current behavior

At the moment there is no way to set a custom search_path in the connection string of the database. This is an hard constraint in certain circumstances and environments where databases are not allowed to be containerized and the database is unique and shared across different applications.

Describe the proposed behavior

I'd like to have a setting in the database settings PREFECT_API_DATABASE_SCHEMA='foo'

Example Use

No response

Additional context

No response

[nich-liu]

This issue should not be closed, as the alembic migrations need to support it as well, so search_path is not sufficient. The original issue raiser is correct that it should be a PREFECT_API_DATABASE_SCHEMA setting.