> that's so you can enter a newline, but agreed, could use a ⌘↵ shortcut or similar.

⌘↩ is the wrong shortcut. On macOS both ⌥↩ and ⇧↩ are the standard shortcuts to add new lines on fields where ↩ would cause an action. If you want to keep ↩ to add a new line, then ⌘↩ would send the message.

Can’t speak for the convention on other OSs, though.