Earlier quoted context omitted.
Serious question: does the concept of a webmaster still exist in 2023? Sites are developed and built in dtap, deployed by gated processes, and in many instances nobody but the deployment agents have access to the actual production servers.
Maybe not, but you could be in a bit of a bubble regarding the average website deployment method. In my experience as a webdev most website are still very much deployed in a way that’s controllable by those who would put up such an alert. The problem is rather political. Any organization with a website relevant enough to make such a popup worthwhile would never agree to have such a popup alienating its largest share…
1. Get fingerprints of the browsers of your superiors (or simply use IP addresses), and don't show the popups on those browsers.
2. Let the script be hosted by a central authority (say eff.org), so they can activate it centrally and the popup appears on many websites at the same time, which will make you look less bad.