[Dashboard] [Controls] Fix inherited input race condition (#154293)

Closes https://github.com/elastic/kibana/issues/154071

## Summary

**Before:**

Before this PR, the dashboard's children would start being
loaded/initialized **before** the control group was necessarily ready -
this caused a race condition where, when the children tried to get their
inherited input, if the control group wasn't quite ready yet, then they
would not receive the control group's filters for their initialization.

So, on first load of a dashboard with one or more controls with
selections, it was possible for the contents of a dashboard to **not
reflect** the control selections, like so:

![Screenshot 2023-04-06 at 1 54 16
PM](https://user-images.githubusercontent.com/8698078/230481821-624221ff-cbee-4288-af24-c7cede312f14.png)

This obviously caused flakiness for the drilldown test, because if the
children in the source dashboard did not receive the inherited input
from the control group, then the drilldown **also** wouldn't pass down
the control group filters.

**After:**

To avoid this race condition, the dashboard now waits until the control
group is ready **before** the children can be loaded - so, when the
children try to get their inherited input, it should **always** contain
the control group's output filters:

![Screenshot 2023-04-06 at 1 59 15
PM](https://user-images.githubusercontent.com/8698078/230484589-a43c3292-3a6b-4f07-8a89-8ec181141024.png)




### Flaky Test Runner

<a
href="https://buildkite.com/elastic/kibana-flaky-test-suite-runner/builds/2099"><img
src="https://user-images.githubusercontent.com/8698078/230492496-d9f6e3c0-5a20-4c1e-bbab-fe90a275229e.png"/></a>

### Checklist

- [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



### 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)

src/plugins/dashboard/public/dashboard_container/embeddable/dashboard_container.tsx

@@ -311,14 +311,14 @@ export class DashboardContainer extends Container<InheritedChildInput, Dashboard
     // update input so the redux embeddable tools get the unwrapped, initial input
     this.updateInput({ ...initialInput });
 
-    // now that the input with the initial panel state has been set, we can tell the container class it's time to start loading children.
-    readyToInitializeChildren$.next(initialInput);
-
     // build Control Group
     if (creationOptions?.useControlGroupIntegration) {
       this.controlGroup = await startControlGroupIntegration.bind(this)(initialInput);
     }
 
+    // now that the input with the initial panel state has been set and the control group is ready, we can tell the container class it's time to start loading children.
+    readyToInitializeChildren$.next(initialInput);
+
     // start diffing dashboard state
     const diffingMiddleware = startDiffingDashboardState.bind(this)({
       useSessionBackup: creationOptions?.useSessionStorageIntegration,

x-pack/test/functional/apps/dashboard/group3/drilldowns/dashboard_to_dashboard_drilldown.ts

@@ -124,8 +124,7 @@ export default function ({ getService, getPageObjects }: FtrProviderContext) {
     await PageObjects.dashboard.waitForRenderComplete();
   };
 
-  // Failing: See https://github.com/elastic/kibana/issues/154071
-  describe.skip('Dashboard to dashboard drilldown', function () {
+  describe('Dashboard to dashboard drilldown', function () {
     describe('Create & use drilldowns', () => {
       before(async () => {
         log.debug('Dashboard Drilldowns:initTests');