[Discover] [ES|QL] Fix ES|QL functional test MKI failure (#195150)

## Summary

This PR attempts to fix the MKI functional test failure from #188816.

Fixes #188816.

### Checklist

- [ ] Any text added follows [EUI's writing
guidelines](https://elastic.github.io/eui/#/guidelines/writing), uses
sentence case text and includes [i18n
support](https://github.com/elastic/kibana/blob/main/packages/kbn-i18n/README.md)
- [ ]
[Documentation](https://www.elastic.co/guide/en/kibana/master/development-documentation.html)
was added for features that require explanation or tutorials
- [x] [Unit or functional
tests](https://www.elastic.co/guide/en/kibana/master/development-tests.html)
were updated or added to match the most common scenarios
- [ ] [Flaky Test
Runner](https://ci-stats.kibana.dev/trigger_flaky_test_runner/1) was
used on any tests changed
- [ ] Any UI touched in this PR is usable by keyboard only (learn more
about [keyboard accessibility](https://webaim.org/techniques/keyboard/))
- [ ] Any UI touched in this PR does not create any new axe failures
(run axe in browser:
[FF](https://addons.mozilla.org/en-US/firefox/addon/axe-devtools/),
[Chrome](https://chrome.google.com/webstore/detail/axe-web-accessibility-tes/lhdoppojpmngadmnindnejefpokejbdd?hl=en-US))
- [ ] If a plugin configuration key changed, check if it needs to be
allowlisted in the cloud and added to the [docker
list](https://github.com/elastic/kibana/blob/main/src/dev/build/tasks/os_packages/docker_generator/resources/base/bin/kibana-docker)
- [ ] This renders correctly on smaller devices using a responsive
layout. (You can test this [in your
browser](https://www.browserstack.com/guide/responsive-testing-on-local-server))
- [ ] This was checked for [cross-browser
compatibility](https://www.elastic.co/support/matrix#matrix_browsers)

### For maintainers

- [ ] This was checked for breaking API changes and was [labeled
appropriately](https://www.elastic.co/guide/en/kibana/master/contributing.html#kibana-release-notes-process)

Co-authored-by: Matthias Wilhelm <matthias.wilhelm@elastic.co>

test/functional/page_objects/discover_page.ts

@@ -597,6 +597,7 @@ export class DiscoverPageObject extends FtrService {
     if (await this.testSubjects.exists('select-text-based-language-btn')) {
       await this.testSubjects.click('select-text-based-language-btn');
       await this.header.waitUntilLoadingHasFinished();
+      await this.waitUntilSearchingHasFinished();
     }
   }
 

x-pack/test_serverless/functional/test_suites/common/discover/esql/_esql_view.ts

@@ -38,9 +38,6 @@ export default function ({ getService, getPageObjects }: FtrProviderContext) {
   };
 
   describe('discover esql view', function () {
-    // see details: https://github.com/elastic/kibana/issues/188816
-    this.tags(['failsOnMKI']);
-
     before(async () => {
       await kibanaServer.savedObjects.cleanStandardList();
       log.debug('load kibana index with default index pattern');