I want my watch to vibrate only and my phone to display badges only...

I've had my iPhone 14 Pro Max since it came out and recently got an Apple Watch Series 9 to accompany it.

I've been trying to customise Notifications and Sounds & Haptics settings on both devices, but I can't get it to work the way I want...

I'd like my Apple Watch Series 9 to only vibrate and my iPhone 14 Pro Max to only display badges:

On the Apple Watch Series 9, there would be no sound or visual display of notifications - only haptics when a notification is received 📳

On the iPhone 14 Pro Max, there would be no sound, haptics or visual display of notifications - only badges when I unlock the device 🔴

Is this set-up possible?

If not, it would be great to hear how I could get as close to this set-up as possible - for context, if this comes across as an unusual set-up, I'm neurodivergent and appreciate simplification 😅

Thanks 🙏🏽