Can I schedule Focus Modes exclusively for my Apple Watch?

Goal: automate low power mode on watch only - I have a medical device that I can’t let my phone go into low power mode. However I want to try to make it through full nights wearing my watch to track sleep

I would still like my phone to be in a DND or sleep mode to not get notifications.. same with my watch

but I don’t want my phone to go into low power, JUST the watch. so if I set the sleep focus filter to low power, the phone will go into low power.

is there a way to schedule a focus for the watch ONLY? Or to change settings for sleep focus on the watch?

I thought I read the watch goes into low power when it’s on sleep automatically but that doesn’t seem true?

thanks!

[Re-Titled by Moderator]