Add database schema with SQLAlchemy async + Alembic migrations

Set up PostgreSQL database layer with async SQLAlchemy 2.0 and asyncpg driver.
Implements 6 core tables (games, routes, pokemon, route_encounters, nuzlocke_runs,
encounters) with foreign keys, indexes, and an initial Alembic migration.

Co-Authored-By: Claude Opus 4.5 <noreply@anthropic.com>

backend/src/app/api/health.py

@@ -1,12 +1,22 @@
 from fastapi import APIRouter
+from sqlalchemy import text
+
+from app.core.database import async_session
 
 router = APIRouter(tags=["health"])
 
 
 @router.get("/health")
 async def health_check():
-    """Health check endpoint."""
-    return {"status": "healthy"}
+    """Health check endpoint with database connectivity verification."""
+    try:
+        async with async_session() as session:
+            await session.execute(text("SELECT 1"))
+        db_status = "connected"
+    except Exception:
+        db_status = "disconnected"
+
+    return {"status": "healthy", "database": db_status}
 
 
 @router.get("/")