Answer
Copying or sharing an invitation link, sending an email invitation or displaying a QR code keeps it in AI until then. These actions do not add a conversation message or change its last-message preview. An empty chat does not gain a waiting preview just because you sent an invitation.
Selecting an existing Hashchats contact in Add People adds them immediately, so the chat moves to People immediately. When someone joins through a link, the same chat moves and records their join. An open chat stays open.
Older installed builds may move a chat when the invitation is sent, and that saved type is shared across devices. Invitations still work between builds. Existing one-person People chats are not moved back just by this update.