feat: scaffold FastAPI backend with ports-and-adapters layout

backend/app/main.py

@@ -0,0 +1,27 @@
+"""Application factory and wiring. No logic lives here."""
+
+from pathlib import Path
+
+from fastapi import FastAPI
+from fastapi.staticfiles import StaticFiles
+
+from app.config import settings
+
+FRONTEND_DIST = Path(__file__).parent / "static"
+
+
+def create_app() -> FastAPI:
+    """Build the FastAPI app: API routes plus the built SPA on one port."""
+    app = FastAPI(title="discovery-by-llm", docs_url=None, redoc_url=None)
+
+    @app.get("/api/health")
+    def health() -> dict[str, str]:
+        return {"status": "ok", "mode": settings.app_mode}
+
+    if FRONTEND_DIST.is_dir():
+        app.mount("/", StaticFiles(directory=FRONTEND_DIST, html=True), name="spa")
+
+    return app
+
+
+app = create_app()