Hi there joey_0411,
There would not be a specific Focus that only pushes notifications to your Apple Watch, however you can achieve this by using this information from Notifications on your Apple Watch:
If your iPhone is locked or asleep, you get notifications on your Apple Watch, unless your Apple Watch is locked.
Once you set up your notification settings for your Apple Watch, all the notifications should go to your Apple Watch as long as your iPhone is locked.
If you are playing games on your iPhone or would like to see this feature added to Focus, then we would encourage you to submit your feedback about this here: Feedback - iPhone - Apple
Cheers!