You can't. You're asking for DRM for the information that you got a positive test. This is impossible. There is no way for what you're asking to be done, website or not - people can repeat and do whatever they want once you know your test status.
So we are back at the point were some medical details are essentially made public which leaves a bitter taste. I am not so sure that there is no way to protect that data at least to some extent.
Most countries didn't even try, while some countries have at least systems in place that try to reduce the privacy impact. Will all these countries ever delete all this fine-grained contact tracing, testing and vaccine status data? Of course not.
In Germany it just made the news that police was unlawfully accessing contact tracing data.
Positive tests for infectious disease have always essentially been made public, yes. This is not new, it's been the case for over a century in most countries.
You have the right to know if you have been in contact with someone that has tested positive, and you have the right to tell other people.
