A single website is running in the background 24/7 [duplicate]

This is a known, common bug in the Screen Time application. It's been around for a few years and it doesn't look like Apple is in any hurry to fix it.

The URL is displayed because it was running in Safari while you were viewing videos.

If you're really concerned about it, or embarassing sites are displayed, just delete the Safari cache and history, they'll go away.