[test] Add drain after typing

Typing seem to be a big issue with this so fix it in general

Bug: none
Change-Id: Idf14af8c1efba63fa110b44766ece75ff8798c39
Reviewed-on: https://chromium-review.googlesource.com/c/devtools/devtools-frontend/+/6263509
Reviewed-by: Alex Rudenko <[email protected]>
Commit-Queue: Nikolay Vitkov <[email protected]>

Author: Lightning00Blade

test/shared/helper.ts

@@ -197,6 +197,7 @@ export const pressKey =
 export const pasteText = async (text: string) => {
   const {frontend} = getBrowserAndPages();
   await frontend.keyboard.sendCharacter(text);
+  await drainFrontendTaskQueue();
 };
 
 // Get a single element handle. Uses `pierce` handler per default for piercing Shadow DOM.