A waiting family needs clear information more than repeated instructions not to worry.

Being told not to worry gives a frightened person nothing to hold. Worry is what fills a gap, so the only thing that reliably lowers it is information: what is known, what is not yet known, and when someone will come back with more. Reassurance without content can make it worse, because it sounds like something is being managed rather than shared.

If you are the one with the news, say those three things and give a time for the next update. If you are waiting, it is fair to ask when you will next hear something. A known interval is easier to sit inside than an open one.