Have you checked that notifications in the Wearable app are active for Messages? You may also need to modify your 'Show phone notifications on watch' options to show alerts even when phone in use.
Also, if you're using Google Messages, are you logged into the web version on an active PC/browser? If so that may be 'intercepting' the notification (since it's acting like the currently-active device) and leaving all other sessions with just an unread, silent notification. Very common with Telegram, too.