Shift+Enter is standard for adding a newline without submitting a message. It’s probably going to confuse a lot of people if Shift+Enter is used to send messages, because it will train the wrong muscle memory. I always reach for shift+enter when I want to be sure that a program is not going to send the message.
Ctrl/Command+Enter is standard for submitting things (chat messages, emails, etc.). Try both keybindings in Discord, Slack, Gmail, Google Chat, Thunderbird, and most other programs.
Edit: Command+Enter works for Discourse posts too.