[Discover] Address flaky tests related to breakdown (elastic#230441)

- Closes elastic#229970
- Closes elastic#229703
- Closes elastic#229867
- Closes elastic#230458
- Closes elastic#230435


### Checklist

- [x] [Flaky Test
Runner](https://ci-stats.kibana.dev/trigger_flaky_test_runner/1) was
used on any tests changed
- [x] The PR description includes the appropriate Release Notes section,
and the correct `release_note:*` label is applied per the
[guidelines](https://www.elastic.co/guide/en/kibana/master/contributing.html#kibana-release-notes-process)
- [x] Review the [backport
guidelines](https://docs.google.com/document/d/1VyN5k91e5OVumlc0Gb9RPa3h1ewuPE705nRtioPiTvY/edit?usp=sharing)
and apply applicable `backport:*` labels.

Author: jughosta

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

@@ -303,10 +303,15 @@ export default function ({ getService, getPageObjects }: FtrProviderContext) {
 
     it('should reset all histogram state when resetting the saved search', async () => {
       await common.navigateToApp('discover');
+      await header.waitUntilLoadingHasFinished();
       await discover.waitUntilSearchingHasFinished();
       await timePicker.setDefaultAbsoluteRange();
+      await header.waitUntilLoadingHasFinished();
+      await discover.waitUntilSearchingHasFinished();
       const savedSearch = 'histogram state';
       await discover.saveSearch(savedSearch);
+      await header.waitUntilLoadingHasFinished();
+      await discover.waitUntilSearchingHasFinished();
       await discover.chooseBreakdownField('extension.keyword');
       await discover.setChartInterval('Second');
       await retry.try(async () => {
@@ -320,8 +325,10 @@ export default function ({ getService, getPageObjects }: FtrProviderContext) {
         });
       });
       await discover.toggleChartVisibility();
+      await header.waitUntilLoadingHasFinished();
       await discover.waitUntilSearchingHasFinished();
       await discover.revertUnsavedChanges();
+      await header.waitUntilLoadingHasFinished();
       await discover.waitUntilSearchingHasFinished();
       await retry.try(async () => {
         const requestData =

src/platform/test/functional/page_objects/discover_page.ts

@@ -229,12 +229,27 @@ export class DiscoverPageObject extends FtrService {
       await this.testSubjects.find('unifiedHistogramBreakdownSelectorSelectorSearch')
     ).type(field);
 
-    const option = await this.find.byCssSelector(
-      `[data-test-subj="unifiedHistogramBreakdownSelectorSelectable"] .euiSelectableListItem[value="${
-        value ?? field
-      }"]`
-    );
-    await option.click();
+    const optionValue = value ?? field;
+    let option;
+
+    await this.retry.try(async () => {
+      option = await this.find.byCssSelector(
+        `[data-test-subj="unifiedHistogramBreakdownSelectorSelectable"] .euiSelectableListItem[value="${optionValue}"]`
+      );
+
+      return Boolean(option);
+    });
+
+    await option!.click();
+    await this.retry.waitFor('the value to be selected', async () => {
+      const breakdownButton = await this.testSubjects.find(
+        'unifiedHistogramBreakdownSelectorButton'
+      );
+      return (
+        (await breakdownButton.getAttribute('data-selected-value')) === optionValue ||
+        (await breakdownButton.getVisibleText()) === field
+      );
+    });
   }
 
   public async clearBreakdownField() {

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

@@ -310,10 +310,15 @@ export default function ({ getService, getPageObjects }: FtrProviderContext) {
 
     it('should reset all histogram state when resetting the saved search', async () => {
       await PageObjects.common.navigateToApp('discover');
+      await PageObjects.header.waitUntilLoadingHasFinished();
       await PageObjects.discover.waitUntilSearchingHasFinished();
       await PageObjects.timePicker.setDefaultAbsoluteRange();
+      await PageObjects.header.waitUntilLoadingHasFinished();
+      await PageObjects.discover.waitUntilSearchingHasFinished();
       const savedSearch = 'histogram state';
       await PageObjects.discover.saveSearch(savedSearch);
+      await PageObjects.header.waitUntilLoadingHasFinished();
+      await PageObjects.discover.waitUntilSearchingHasFinished();
       await PageObjects.discover.chooseBreakdownField('extension.keyword');
       await PageObjects.discover.setChartInterval('Second');
       await retry.try(async () => {
@@ -327,8 +332,10 @@ export default function ({ getService, getPageObjects }: FtrProviderContext) {
         });
       });
       await PageObjects.discover.toggleChartVisibility();
+      await PageObjects.header.waitUntilLoadingHasFinished();
       await PageObjects.discover.waitUntilSearchingHasFinished();
       await PageObjects.discover.revertUnsavedChanges();
+      await PageObjects.header.waitUntilLoadingHasFinished();
       await PageObjects.discover.waitUntilSearchingHasFinished();
       await retry.try(async () => {
         const requestData =