chore(schema): generate PostgreSQL schema documentation #417

Goal

Make the deployed PostgreSQL schema discoverable and reviewable without treating EF Core's CLR model as the complete source of truth.

Scope

• Generate a readable ERD committed under docs/.
• Generate a companion schema catalog with tables, columns/types/nullability/defaults, primary and unique keys, foreign keys/delete actions, check constraints, indexes (including predicates and expression indexes), and relationships.
• Derive both artifacts from an ephemeral PostgreSQL database migrated by the repository migrations, so raw SQL migration details such as expression/partial indexes are represented.
• Provide a deterministic developer/CI-friendly generator and a check mode that detects stale generated artifacts.
• Add tests/guards for generator determinism and coverage of PostgreSQL-specific index details.
• Add an AGENTS.md rule: every schema migration must regenerate and commit the documentation; generated artifacts are never hand-edited.

Non-goals

• No changes to application data model or production database.
• No live database credentials or production schema introspection.
• No editing or regenerating the frozen InitialCreate migration.

Acceptance criteria

• The generated ERD is readable in GitHub and links to the complete catalog.
• The catalog includes every table, FK relationship, PK/unique key, check constraint, index definition, and index predicate/expression in the migration-created Postgres schema.
• A clean checkout can generate the exact committed output using documented prerequisites.
• CI/test verification fails when the generated documentation is stale after a schema change.
• The workflow and maintenance rule are documented.