The first preparations for Locked Chats are now showing up in the ChatGPT web app as well
"Lock sensitive chats - Create a PIN to lock selected chats and hide them from your sidebar and search. Once locked, new messages in that chat won’t be used to personalize regular chats."
Locked Chats in ChatGPT - the new Android app beta version adds more details about the upcoming feature for hiding chats in "Projects → Locked chats" and a new "Unlock chat" option (the chat will be removed from Locked Chats and shown in your sidebar again)
"Lock a chat to keep its title and content out of view in your regular sidebar, history, and search results. You’ll need your PIN or device unlock method to open it."