Screen Time restrictions do not work on links in Messages

I currently have Screen Time app and content restrictions setup for my child's iPhone, which includes a limited amount of time for Safari and for the YouTube website (not the app, which is not installed). My child has figured out that if they just send themselves a message in Messages with the link to a YouTube video, they can watch that video from within Messages via the link preview, even after the Safari and youtube.com Screen Time limits have been exceeded and blocking is enabled. I don't want to place Screen Time restrictions on Messages, because it is a safety issue.

How can I prohibit my child from watching YouTube videos from within Messages after Screen Time limits have been reached?