feat: merge cartsnitch/api into api/ subdirectory

Consolidate API gateway service into monorepo.
Squashed from https://github.com/cartsnitch/api main (89bacb1).

Co-Authored-By: Paperclip <noreply@paperclip.ing>

src/cartsnitch_api/main.py

@@ -0,0 +1,62 @@
+"""FastAPI app factory for CartSnitch API Gateway."""
+
+from contextlib import asynccontextmanager
+
+from fastapi import FastAPI
+
+from cartsnitch_api.auth.routes import router as auth_router
+from cartsnitch_api.middleware.cors import add_cors_middleware
+from cartsnitch_api.middleware.error_handler import add_error_handlers, add_error_monitor_middleware
+from cartsnitch_api.middleware.rate_limit import add_rate_limit_middleware
+from cartsnitch_api.routes.alerts import router as alerts_router
+from cartsnitch_api.routes.coupons import router as coupons_router
+from cartsnitch_api.routes.health import router as health_router
+from cartsnitch_api.routes.prices import router as prices_router
+from cartsnitch_api.routes.products import router as products_router
+from cartsnitch_api.routes.public import router as public_router
+from cartsnitch_api.routes.purchases import router as purchases_router
+from cartsnitch_api.routes.scraping import router as scraping_router
+from cartsnitch_api.routes.shopping import router as shopping_router
+from cartsnitch_api.routes.stores import router as stores_router
+
+
+@asynccontextmanager
+async def lifespan(app: FastAPI):
+    # TODO: initialize DB session pool, Redis connection, service clients
+    yield
+    # TODO: cleanup connections
+
+
+def create_app() -> FastAPI:
+    app = FastAPI(
+        title="CartSnitch API",
+        description="Grocery price tracking and shrinkflation detection API",
+        version="0.1.0",
+        lifespan=lifespan,
+    )
+
+    # Middleware (order matters — outermost first)
+    add_cors_middleware(app)
+    add_error_monitor_middleware(app)
+    add_rate_limit_middleware(app)
+
+    # Exception handlers
+    add_error_handlers(app)
+
+    # Routers
+    app.include_router(health_router)
+    app.include_router(auth_router)
+    app.include_router(stores_router)
+    app.include_router(purchases_router)
+    app.include_router(products_router)
+    app.include_router(prices_router)
+    app.include_router(coupons_router)
+    app.include_router(shopping_router)
+    app.include_router(alerts_router)
+    app.include_router(scraping_router)
+    app.include_router(public_router)
+
+    return app
+
+
+app = create_app()