Problem

When creating our initial migration to bootstrap the database, we hard-code the schema name to public.

Solution

Do not set the schema name at all in the initial bootstrap script.
Allow this to be overridden via search_path in the connection string.

https://www.postgresql.org/docs/current/runtime-config-client.html

Private Link

V1 PR: https://github.com/coder/v1/pull/13216
v1 Issue: https://github.com/coder/v1/issues/13040