[Dashboard] Change Inspector on dashboard to use push flyout (#207750)

## Summary

This PR changes the inspector flyout to be a push flyout and highlights
the panel which is inspected.
![Screenshot 2025-01-22 at 13 19
21](https://github.com/user-attachments/assets/b8668d21-a323-41f0-9128-64c511e26347)
Closes: #148993

src/platform/plugins/private/presentation_panel/public/panel_actions/inspect_panel_action/inspect_panel_action.ts

@@ -15,6 +15,7 @@ import {
   getTitle,
   PublishesTitle,
   HasParentApi,
+  apiHasUniqueId,
 } from '@kbn/presentation-publishing';
 import { Action, IncompatibleActionError } from '@kbn/ui-actions-plugin/public';
 import { ACTION_INSPECT_PANEL } from './constants';
@@ -62,6 +63,7 @@ export class InspectPanelAction implements Action<EmbeddableApiContext> {
       });
     const session = inspector.open(adapters, {
       title: panelTitle,
+      flyoutType: 'push',
       options: {
         fileName: panelTitle,
       },
@@ -71,6 +73,12 @@ export class InspectPanelAction implements Action<EmbeddableApiContext> {
     });
 
     // send the overlay ref to the parent API if it is capable of tracking overlays
-    if (tracksOverlays(embeddable.parentApi)) embeddable.parentApi?.openOverlay(session);
+    if (tracksOverlays(embeddable.parentApi)) {
+      const openOverlayOptions = apiHasUniqueId(embeddable)
+        ? { focusedPanelId: embeddable.uuid }
+        : undefined;
+
+      embeddable.parentApi?.openOverlay(session, openOverlayOptions);
+    }
   }
 }

src/platform/plugins/shared/inspector/public/plugin.tsx

@@ -115,6 +115,7 @@ export class InspectorPublicPlugin implements Plugin<Setup, Start> {
         {
           'data-test-subj': 'inspectorPanel',
           closeButtonProps: { 'aria-label': closeButtonLabel },
+          type: options.flyoutType,
         }
       );
     };

src/platform/plugins/shared/inspector/public/types.ts

@@ -8,6 +8,7 @@
  */
 
 import { OverlayRef } from '@kbn/core/public';
+import { EuiFlyoutProps } from '@elastic/eui';
 import { Adapters } from '../common';
 
 /**
@@ -60,6 +61,7 @@ export interface InspectorViewDescription {
 export interface InspectorOptions {
   title?: string;
   options?: unknown;
+  flyoutType?: EuiFlyoutProps['type'];
 }
 
 export type InspectorSession = OverlayRef;