Refactor database implementation to use PostgreSQL instead of MongoDB (#289)

Fixes #228

## Motivation and Context

See #19

## How Has This Been Tested?

- Run locally
- Run in docker compose
- Run infra in minikube
- Unit and integration tests all passing :)

## Breaking Changes

Yes: users will not be able to access any data they used to have in
custom mongodb. We are accepting this breaking change, given the
registry is in experimental development status.

## Types of changes
<!-- What types of changes does your code introduce? Put an `x` in all
the boxes that apply: -->
- [ ] Bug fix (non-breaking change which fixes an issue)
- [ ] New feature (non-breaking change which adds functionality)
- [x] Breaking change (fix or feature that would cause existing
functionality to change)
- [ ] Documentation update

## Checklist
<!-- Go over all the following points, and put an `x` in all the boxes
that apply. -->
- [x] I have read the [MCP
Documentation](https://modelcontextprotocol.io)
- [x] My code follows the repository's style guidelines
- [x] New and existing tests pass locally
- [x] I have added appropriate error handling
- [x] I have added or updated documentation as needed

## Additional context

I have not implemented connection pooling support for simplicity, and
because cloudnative-pg already provides built-in connection pooling with
pgBouncer so if we want it later we can switch to this endpoint easily.

.env.example

@@ -6,8 +6,9 @@ MCP_REGISTRY_VERSION=dev
 MCP_REGISTRY_LOG_LEVEL=info
 
 # Database configuration
-MCP_REGISTRY_DATABASE_TYPE=mongodb
-MCP_REGISTRY_DATABASE_URL=mongodb://username:password@localhost:27017
+# Supported types: postgresql, memory
+MCP_REGISTRY_DATABASE_TYPE=postgresql
+MCP_REGISTRY_DATABASE_URL=postgres://username:password@localhost:5432/mcp-registry
 MCP_REGISTRY_DATABASE_NAME=mcp-registry
 MCP_REGISTRY_COLLECTION_NAME=servers_v2