In the chat system, stars and pins are retained when moved to another room. This is probably a bug. Here a picture:
When a room owner pins a message, they can move it to another room, and they cannot unpin it. However when a starred message is moved to another room, the user can unstar it in the room it was moved to.
Conversation source: https://chat.meta.stackexchange.com/transcript/message/2412448#2412448