Find a flow's declared inputs and outputs in the global search

/search lists each input and batch output under its qualified message,
and picking one opens the flow on the label's id, which the editor now
treats like a click on the label: it opens the flow's settings.

backend/tests/api/routes/test_search.py

@@ -61,6 +61,29 @@ def test_index_reaches_inside_flows_and_dashboards(
     assert found[("widget", "hall", "temperature")]["kind"] == "stat"
 
 
+def test_index_lists_a_flows_inputs_and_outputs(
+    client: TestClient, superuser_token_headers: dict[str, str]
+) -> None:
+    """Named by the qualified message, which is the label the canvas draws."""
+    client.put(
+        f"{FLOWS}/fit",
+        headers=superuser_token_headers,
+        json={
+            "name": "fit",
+            "mode": "batch",
+            "inputs": [{"spec": {"name": "epochs", "dtype": "int"}}],
+            "outputs": ["accuracy"],
+        },
+    )
+
+    entries = client.get(f"{PREFIX}/", headers=superuser_token_headers).json()
+    found = {(e["category"], e["name"]): e for e in entries if e["parent"] == "fit"}
+
+    assert found[("input", "fit.epochs")]["title"] == "epochs"
+    assert found[("input", "fit.epochs")]["kind"] == "int"
+    assert found[("output", "fit.accuracy")]["title"] == "accuracy"
+
+
 def test_secrets_are_named_only_to_a_superuser(
     client: TestClient,
     superuser_token_headers: dict[str, str],