The Last Contacted property updates automatically with the last date and time of a chat conversation, call, sales email, or meeting logged on a contact record. It is set automatically by Hubspot and is a read-only property, meaning that we are not able to update the property value manually.
I would highly recommend submitting this product feedback to the ideas forum.
Our product team, who monitors the forum regularly, can read your specific use case and understand why this would be a useful functionality or change. It also helps other customers facing the same issue to advocate for its implementation on your behalf by upvoting on the thread as well.