[SharedUX] Remove usage of deprecated React rendering utilities (#180516)

## Summary

Partially addresses https://github.com/elastic/kibana-team/issues/805

Follows https://github.com/elastic/kibana/pull/180003

These changes come up from searching in the code and finding where
certain kinds of deprecated AppEx-SharedUX modules are imported.
**Reviewers: Please interact with critical paths through the UI
components touched in this PR, ESPECIALLY in terms of testing dark mode
and i18n.**

This focuses on code within AppEx-SharedUX. [Reporting changes are
separate](https://github.com/elastic/kibana/pull/).

<img width="1107" alt="image"
src="c0d2ce08-ac35-45a7-8192-0b2256fceb0e">

### Checklist

Delete any items that are not applicable to this PR.

- [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
- [ ] 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)

examples/ui_action_examples/kibana.jsonc

@@ -10,8 +10,6 @@
     "requiredPlugins": [
       "uiActions"
     ],
-    "requiredBundles": [
-      "kibanaReact"
-    ]
+    "requiredBundles": []
   }
 }

examples/ui_action_examples/public/hello_world_action.tsx

@@ -8,14 +8,12 @@
 
 import React from 'react';
 import { EuiText, EuiModalBody, EuiButton } from '@elastic/eui';
-import { OverlayStart } from '@kbn/core/public';
-import { toMountPoint } from '@kbn/kibana-react-plugin/public';
+import { CoreStart } from '@kbn/core/public';
+import { toMountPoint } from '@kbn/react-kibana-mount';
 
 export const ACTION_HELLO_WORLD = 'ACTION_HELLO_WORLD';
 
-interface StartServices {
-  openModal: OverlayStart['openModal'];
-}
+type StartServices = Pick<CoreStart, 'overlays' | 'analytics' | 'i18n' | 'theme'>;
 
 export const createHelloWorldActionDefinition = (
   getStartServices: () => Promise<StartServices>
@@ -24,15 +22,16 @@ export const createHelloWorldActionDefinition = (
   type: ACTION_HELLO_WORLD,
   getDisplayName: () => 'Hello World!',
   execute: async () => {
-    const { openModal } = await getStartServices();
-    const overlay = openModal(
+    const { overlays, ...startServices } = await getStartServices();
+    const overlay = overlays.openModal(
       toMountPoint(
         <EuiModalBody>
           <EuiText data-test-subj="helloWorldActionText">Hello world!</EuiText>
           <EuiButton data-test-subj="closeModal" onClick={() => overlay.close()}>
             Close
           </EuiButton>
-        </EuiModalBody>
+        </EuiModalBody>,
+        startServices
       )
     );
   },

examples/ui_action_examples/public/plugin.ts

@@ -29,14 +29,14 @@ export class UiActionExamplesPlugin
   ) {
     uiActions.registerTrigger(helloWorldTrigger);
 
-    const helloWorldAction = createHelloWorldActionDefinition(async () => ({
-      openModal: (await core.getStartServices())[0].overlays.openModal,
-    }));
+    const helloWorldAction = createHelloWorldActionDefinition(
+      async () => (await core.getStartServices())[0]
+    );
 
     uiActions.addTriggerAction(helloWorldTrigger.id, helloWorldAction);
   }
 
-  public start(core: CoreStart, plugins: UiActionExamplesStartDependencies) {}
+  public start(_core: CoreStart, _plugins: UiActionExamplesStartDependencies) {}
 
   public stop() {}
 }

examples/ui_action_examples/tsconfig.json

@@ -14,8 +14,8 @@
     "target/**/*",
   ],
   "kbn_references": [
-    "@kbn/kibana-react-plugin",
     "@kbn/ui-actions-plugin",
     "@kbn/core",
+    "@kbn/react-kibana-mount",
   ]
 }