refactor: align backend layout and supabase infra

Consolidate backend modules/tests under the backend package while syncing Supabase compose/env config and related plans.

backend/tests/integration/test_mobile_app_skeleton.py

@@ -0,0 +1,39 @@
+from __future__ import annotations
+
+from fastapi.testclient import TestClient
+
+from app import app
+
+
+def test_app_health_returns_envelope() -> None:
+    client = TestClient(app)
+
+    response = client.get("/health")
+
+    assert response.status_code == 200
+    body = response.json()
+    assert body["status"] == "ok"
+
+
+def test_mobile_router_health_returns_envelope() -> None:
+    client = TestClient(app)
+
+    response = client.get("/api/v1/health")
+
+    assert response.status_code == 200
+    body = response.json()
+    assert body["status"] == "ok"
+
+
+def test_not_found_returns_error_envelope() -> None:
+    client = TestClient(app)
+
+    response = client.get("/missing-route")
+
+    assert response.status_code == 404
+    assert response.headers["content-type"].startswith("application/problem+json")
+    body = response.json()
+    assert body["type"] == "about:blank"
+    assert body["title"] == "Not Found"
+    assert body["status"] == 404
+    assert body["detail"] == "Not Found"