Kibana version:
9.1/main

Describe the bug:
Prerequisite: feature flag newDataViewPickerEnabled is enabled

When user does not have write permission, data view manager allows users to make changes to data views (top 2 buttons are visible)

Steps to reproduce:

1. Create a test user without access to indices
2. Go to Kibana, go to any pages that data view manager is accessible (host page, timeline etc.)
3. Click data view picker, noticed the top 2 buttons to modify data views are available

Expected behavior:
Data view manager should micmic the ui in discover when user does not have proper priviledges

Screenshots (if relevant):

Errors in browser console (if relevant):

Provide logs and/or server output (if relevant):

Any additional context: