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/tasks.md

@@ -0,0 +1,27 @@
+## 1. Database Initialization
+
+- [x] 1.1 Create `init_database()` function in `apps/api/src/database.py`
+- [x] 1.2 Add alembic programmatic upgrade call
+- [x] 1.3 Add connection retry logic with backoff
+- [x] 1.4 Modify startup event to call `init_database()` before seeding
+- [x] 1.5 Update seed functions to check table existence first
+
+## 2. Error Handling and Logging
+
+- [x] 2.1 Add clear error messages for connection failures
+- [x] 2.2 Add clear error messages for missing tables
+- [x] 2.3 Add clear error messages for auth failures
+- [x] 2.4 Log migration status on startup
+
+## 3. Docker Integration
+
+- [x] 3.1 Update Dockerfile to wait for database readiness
+- [x] 3.2 Update docker-compose files with init order
+- [x] 3.3 Add health check script for database
+
+## 4. Testing
+
+- [x] 4.1 Test with fresh database (no tables)
+- [x] 4.2 Test with existing database (migrations already applied)
+- [x] 4.3 Test database connection failure handling
+- [x] 4.4 Run quality gates (ruff, mypy, pytest)