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)

apps/api/wait-for-db.sh

@@ -0,0 +1,25 @@
+#!/bin/sh
+# wait-for-db.sh - Wait for PostgreSQL to be ready
+
+set -e
+
+host="${POSTGRES_HOST:-postgres}"
+port="${POSTGRES_PORT:-5432}"
+max_attempts="${DB_MAX_ATTEMPTS:-30}"
+wait_seconds="${DB_WAIT_SECONDS:-2}"
+
+echo "Waiting for database at ${host}:${port}..."
+
+attempt=1
+while ! nc -z "${host}" "${port}"; do
+    if [ "${attempt}" -ge "${max_attempts}" ]; then
+        echo "ERROR: Database not available after ${max_attempts} attempts. Exiting."
+        exit 1
+    fi
+    echo "  Attempt ${attempt}/${max_attempts}: Database not ready yet, waiting ${wait_seconds}s..."
+    sleep "${wait_seconds}"
+    attempt=$((attempt + 1))
+done
+
+echo "Database is ready!"
+exec "$@"