feat: add automatic database initialization and recovery

- Add init_database() with alembic programmatic API and retry logic
- Add connection retry with exponential backoff (5 attempts)
- Improve error messages for connection/auth failures
- Add table existence check before seeding data
- Update startup event to run migrations before seeding
- Add wait-for-db.sh script for Docker containers
- Update Docker and docker-compose configurations

Quality gates: ruff ✓, mypy ✓, unit tests (8 passed)

openspec/changes/database-setup-recovery/proposal.md

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+## Why
+
+The application currently fails to start when database tables are missing or migrations haven't been applied. This creates a poor deployment experience and requires manual intervention. We need automatic database initialization, migration management, and seed data handling to ensure the application starts reliably in any environment.
+
+## What Changes
+
+- **Auto-run migrations on startup** instead of requiring manual `alembic upgrade head`
+- **Improve startup error handling** with clear error messages when DB is unavailable
+- **Add database readiness checks** before attempting migrations or seeding
+- **Seed data management** with proper handling of missing tables
+- **Better database initialization** in Docker environments
+
+## Capabilities
+
+### New Capabilities
+- `database-initialization`: Automatic database setup including migrations and seed data
+
+### Modified Capabilities
+- `docker-infrastructure`: Add database initialization scripts and health checks
+
+## Impact
+
+- `apps/api/src/main.py`: Add startup database initialization
+- `apps/api/src/database.py`: Add connection health checks
+- `apps/api/Dockerfile`: Add init scripts
+- `docker-compose.yml` and `docker-compose.traefik.yml`: Update startup behavior