Failed to load dashboard - Permissions needed: dashboard:read

### What happened? We have a Grafana instance configured with multiple organizations, as well as users who have access to multiple of those organizations, i.e. users can switch between them using the drop-down at the top of the navigation panel. When switching an organization, a user cannot access the dashboard of the switched-to organization, until some time passes. The following screenshots are from a demo setup with organizations `One` and `Two`, each of which has a default dashboard as its `Home`, in order to minimize clicking that is needed to reproduce the problem. The following screenshot belongs to two clicks of the `Home` link in organization `One`. <img width="1095" height="155" alt="Image" src="https://github.com/user-attachments/assets/3f00eaf6-b1d5-4a58-9383-b01d3f4c82e5" /> Both GETs of `https://grafana.demo/api/dashboards/uid/2992a2d3f14c825cf548b060d30aa99c` are successful, rendering the dashboard just fine. The next screenshot belongs to a switch to organization `Two`. <img width="1097" height="1012" alt="Image" src="https://github.com/user-attachments/assets/acdf3254-6368-4e9d-8d3a-a05f4e474e1c" /> The GET of `https://grafana.demo/api/dashboards/uid/9b6a38441272b1dd1208ce68a478dac7` at `12:28:40` is unsuccessful (HTTP 403) with payload ``` { "accessErrorId": "ACE7670784547", "message": "You'll need additional permissions to perform this action. Permissions needed: dashboards:read", "title": "Access denied" } ``` The above shows as: <img width="737" height="96" alt="Image" src="https://github.com/user-attachments/assets/1acc1a6a-5748-42d1-a6af-79a0ac006463" /> The next screenshot shows multiple clicks on the `Home` link in the `Two` organization, all yielding the same permission errors for `https://grafana.demo/api/dashboards/uid/9b6a38441272b1dd1208ce68a478dac7`, until there is a successful request at `12:30:15`. <img width="1083" height="1009" alt="Image" src="https://github.com/user-attachments/assets/6163ce85-09a2-478b-9ae6-cb73ead…