LEOs do it all the time. Courts have even ruled repeatedly that they can be as disingenuous as they wish if it causes someone to reveal evidence or incriminate themselves, even if circumstantially.
But in the case of a traffic stop, you have the right to remain silent. How could someone possibly know that they were infected by a government-created virus? I’m not sure how this could be contorted to be considered legal. They’re literally saying that you’re guilty just for going to the website. That’s like arresting someone for looking at a home that’s a known drug dealer’s residence.