When they find a missing person who they had issued a public appeal for, they publish that they've been found 'safe and well', albeit with no further details.
Otherwise when this person reappeared and tried to go about their normal life, they'd be receiving sightings left right and centre from the public, and the formerly missing person would probably feel uncomfortable with well meaning strangers taking photos as evidence of such sightings.
One recent Met Police case where this happened was Owami Davies
www.telegraph.co.uk/news/2022/08/23/owami-davies-found-safe-eight-weeks-vanished/
No news just means they haven't any updates they want to put into the public domain. We don't know if they've had zero leads or they've had lots and are about to make a breakthrough and don't want to spook CM & MG.