Tab Search: Add API performance metric

Matching src-public CL:
https://chromium-review.googlesource.com/c/chromium/src/+/2432589

Bug: 1099917
Change-Id: I19496be097ef9714e0e46872ff6966e54e442086
Reviewed-on: https://chrome-internal-review.googlesource.com/c/chrome/browser/resources/tab_search/+/3291206Reviewed-by: John Lee <johntlee@chromium.org>
Cr-Commit-Position: refs/heads/master@{#819623}

chrome/browser/resources/tab_search_merge/app.js

@@ -148,7 +148,12 @@ export class TabSearchAppElement extends PolymerElement {
 
   /** @private */
   updateTabs_() {
+    const getTabsStartTimestamp = Date.now();
     this.apiProxy_.getProfileTabs().then(({profileTabs}) => {
+      chrome.metricsPrivate.recordTime(
+          'Tabs.TabSearch.WebUI.TabListDataReceived',
+          Math.round(Date.now() - getTabsStartTimestamp));
+
       // Prior to the first load |this.openTabs_| has not been set. Record the
       // time it takes for the initial list of tabs to render.
       if (!this.openTabs_) {