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.

internal/database/database.go

@@ -36,8 +36,8 @@ type ConnectionType string
 const (
 	// ConnectionTypeMemory represents an in-memory database connection
 	ConnectionTypeMemory ConnectionType = "memory"
-	// ConnectionTypeMongoDB represents a MongoDB database connection
-	ConnectionTypeMongoDB ConnectionType = "mongodb"
+	// ConnectionTypePostgreSQL represents a PostgreSQL database connection
+	ConnectionTypePostgreSQL ConnectionType = "postgresql"
 )
 
 // ConnectionInfo provides information about the database connection
@@ -47,7 +47,7 @@ type ConnectionInfo struct {
 	// IsConnected indicates whether the database is currently connected
 	IsConnected bool
 	// Raw provides access to the underlying connection object, which will vary by implementation
-	// For MongoDB, this will be *mongo.Client
+	// For PostgreSQL, this will be *pgx.Conn
 	// For MemoryDB, this will be map[string]*model.MCPRegistry
 	Raw any
 }