Path of Exile doesn’t currently offer a feature to appear offline. There are a couple things to consider though:
Do Not Disturb (DND): You can activate DND mode to mute all incoming messages and whispers. This won’t hide your online status, but it will prevent people from contacting you.
AFK Status: You can use the /afk command to set an Away From Keyboard message. This will only be visible to people who try to message you directly.
Here’s a summary:
Appear Offline: Not supported
Silence Messages: Use Do Not Disturb mode
Set Away Message: Use /afk command (visible only to those who message you)