[Chrome Next] Migrate content connectors to AppHeader (#289612)

## Summary

This PR migrates `Content connectors` pages to the new `AppHeader`.

Part of: elastic/kibana-team#3945

### Visuals


https://github.com/user-attachments/assets/a51f7dbd-d648-486f-8e4d-c10cd3d5a961

Author: kowalczyk-krzysztof

x-pack/platform/plugins/shared/content_connectors/moon.yml

@@ -63,6 +63,7 @@ dependsOn:
   - '@kbn/logging'
   - '@kbn/shared-ux-ai-components'
   - '@kbn/deeplinks-management'
+  - '@kbn/app-header'
   - '@kbn/ui-callout'
   - '@kbn/usage-collection-plugin'
   - '@kbn/core-logging-server-mocks'

x-pack/platform/plugins/shared/content_connectors/public/api/connector/cached_fetch_connector_by_id_api_logic.ts

@@ -40,6 +40,7 @@ export interface CachedFetchConnectorByIdApiLogicActions {
   setTimeoutId(id: NodeJS.Timeout): { id: NodeJS.Timeout };
   startPolling(connectorId: string): { connectorId: string };
   stopPolling(): void;
+  updateConnectorData(update: Partial<Connector>): Partial<Connector>;
 }
 export interface CachedFetchConnectorByIdApiLogicValues {
   connectorData: Connector | null;
@@ -62,6 +63,7 @@ export const CachedFetchConnectorByIdApiLogic = kea<
     setTimeoutId: (id) => ({ id }),
     startPolling: (connectorId) => ({ connectorId }),
     stopPolling: true,
+    updateConnectorData: (update) => update,
   },
   connect: {
     actions: [FetchConnectorByIdApiLogic, ['apiSuccess', 'apiError', 'apiReset', 'makeRequest']],
@@ -123,6 +125,13 @@ export const CachedFetchConnectorByIdApiLogic = kea<
             ? currentState
             : newConnectorData.connector ?? null;
         },
+        updateConnectorData: (currentState, update) => {
+          if (!currentState) {
+            return currentState;
+          }
+          const nextState = { ...currentState, ...update };
+          return isEqual(currentState, nextState) ? currentState : nextState;
+        },
       },
     ],
     connectorId: [