Apple Watch & Emergency Bypass / Custom Tones

Have you tried using Mirror iPhone on the Watch message notifications?

I used to have it as mirror and every message that came in vibrated and sounded on both my iPhone and Watch.

On the Watch app on your iPhone

Watch>My Watch>Notifications>Messages

Mirror my iPhone

This works for email as well

Your observed alerting doesn’t seem right and I’m pretty sure I get alerts on all my devices when they are in screen dark mode, there is a regular barrage of dings and beeps as each one tells me about the same event. If anything it should be your watch which doesn’t make an audible alert if the phone is active in your hand, not the other way around. See Notifications on your Apple Watch - Apple Support for Apple’s description of how it is intended to work.

I just tried to test here but there’s a problem because all my devices do iMessage rather than true SMS. However, it looks like your observation might be correct and for some reason only my watch alerted to iMessage from my work phone to my (locked and idle) personal phone. I’m going to make a wild and untested guess this could be a bug, or maybe fallout from security settings to reduce the impact of the lock screen hacks so it might be worth checking these.