Public Dashboards: Unauthorized Popup issue is still present with certain visualizations

### What happened? The problem is probably well known as there exist some other issues already which as far as I could tell, are closed by now since the issues were fixed. Unfortunately, I still get the unauthorized popup using the latest Grafana v12.2.0 (92f1fba9b4) <img width="505" height="130" alt="Image" src="https://github.com/user-attachments/assets/f7d210cd-cf92-47c8-9ef6-12d52336e395" /> It is probably related to this visualization plugin: https://github.com/VolkovLabs/business-calendar Which triggers these annotation calls: <img width="597" height="24" alt="Image" src="https://github.com/user-attachments/assets/998a3db8-8904-44f4-a23a-af5b101518e5" /> ### What did you expect to happen? Using the public Dashboard without interruptions from this popup. ### Did this work before? No, as far as I know not. ### How do we reproduce it? 1. Create a dashboard with a Business Calendar panel, as the Datasource I used postgres 2. Create a Public Dashboard 3. Access this dashboard in a private tab and move forward/backward in the calendar, every time the popup Unauthorized will appear ### Is the bug inside a dashboard panel? This isn't really neccessary, it happens reproduceable with the Business Calendar panel which triggers these annotation requests ### Environment (with versions)? Grafana: Grafana v12.2.0 (92f1fba9b4) OS: Linux (RHEL) Browser: Firefox 143.0.1 (64-Bit) ### Grafana platform? Docker ### Datasource(s)? _No response_