Fix sending search snowplow events (#31762)

e2e/test/scenarios/onboarding/search/search.cy.spec.js

-import { restore } from "e2e/support/helpers";
+import {
+  describeWithSnowplow,
+  enableTracking,
+  expectGoodSnowplowEvents,
+  expectNoBadSnowplowEvents,
+  resetSnowplow,
+  restore,
+} from "e2e/support/helpers";
 import { ORDERS_QUESTION_ID } from "e2e/support/cypress_sample_instance_data";
 
-describe("scenarios > auth > search", () => {
+describe("scenarios > search", () => {
   beforeEach(restore);
 
   describe("universal search", () => {
@@ -63,6 +70,28 @@ describe("scenarios > auth > search", () => {
   });
 });
 
+describeWithSnowplow("scenarios > search", () => {
+  const PAGE_VIEW_EVENT = 1;
+
+  beforeEach(() => {
+    restore();
+    resetSnowplow();
+    cy.signInAsAdmin();
+    enableTracking();
+  });
+
+  afterEach(() => {
+    expectNoBadSnowplowEvents();
+  });
+
+  it("should send snowplow events for global search queries", () => {
+    cy.visit("/");
+    expectGoodSnowplowEvents(PAGE_VIEW_EVENT);
+    cy.findByPlaceholderText("Search…").type("Orders").blur();
+    expectGoodSnowplowEvents(PAGE_VIEW_EVENT + 1); // new_search_query
+  });
+});
+
 function getProductsSearchResults() {
   cy.findByText("Products");
   // This part about the description reproduces metabase#20018

snowplow/iglu-client-embedded/schemas/com.metabase/search/jsonschema/1-0-0

@@ -17,11 +17,14 @@
     },
     "runtime_milliseconds": {
       "description": "Number of milliseconds it took to successfully run the search query",
-      "type": "integer",
+      "type": [
+        "integer",
+        "null"
+      ],
       "minimum": 0,
       "maximum": 2147483647
     }
   },
-  "required": ["runtime"],
+  "required": ["event"],
   "additionalProperties": true
 }