The messaging system is already in the process of being removed, the ability to send/receive messages has been stopped for a while now. Going to the messages page https://www.twitch.tv/messages/inbox will just display:
I’m not sure if there was any big announcement in the way they usually announce things, a lot of people had no clue it was happening until days before, but the messages page did show a notice when you visited this page in the weeks or months leading up to its removal that it was going to happen.