[9.1] [Discover] Fix flaky test - query should support querying on nested fields (#231692) (#231736)

# Backport

This will backport the following commits from `main` to `9.1`:
- [[Discover] Fix flaky test - query should support querying on nested
fields (#231692)](#231692)

<!--- Backport version: 9.6.6 -->

### Questions ?
Please refer to the [Backport tool
documentation](https://github.com/sorenlouv/backport)

<!--BACKPORT [{"author":{"name":"Ania
Kowalska","email":"[email protected]"},"sourceCommit":{"committedDate":"2025-08-14T06:13:22Z","message":"[Discover]
Fix flaky test - query should support querying on nested fields
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Fix flaky test - query should support querying on nested
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Fix flaky test - query should support querying on nested fields
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Fix flaky test - query should support querying on nested fields
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BACKPORT-->

Co-authored-by: Ania Kowalska <[email protected]>

Author: kibanamachine

src/platform/test/functional/apps/discover/group1/_discover.ts

@@ -193,6 +193,10 @@ export default function ({ getService, getPageObjects }: FtrProviderContext) {
       it('should support querying on nested fields', async function () {
         await queryBar.setQuery('nestedField:{ child: nestedValue }');
         await queryBar.submitQuery();
+
+        await header.waitUntilLoadingHasFinished();
+        await discover.waitUntilSearchingHasFinished();
+
         await retry.try(async function () {
           expect(await discover.getHitCount()).to.be('1');
         });

x-pack/platform/test/serverless/functional/test_suites/discover/group1/_discover.ts

@@ -197,6 +197,10 @@ export default function ({ getService, getPageObjects }: FtrProviderContext) {
       it('should support querying on nested fields', async function () {
         await queryBar.setQuery('nestedField:{ child: nestedValue }');
         await queryBar.submitQuery();
+
+        await PageObjects.header.waitUntilLoadingHasFinished();
+        await PageObjects.discover.waitUntilSearchingHasFinished();
+
         await retry.try(async function () {
           expect(await PageObjects.discover.getHitCount()).to.be('1');
         });