Can we have the watch respect DND (Do Not Disturb) when it's set on an Android phone?

I have a Pixel 3 with a Pixel stand that automatically puts the phone on DND mode, but the watch still vibrates on notifications even though I don't even see them on the phone itself. If the watch would respect DND, it would all work automatically as I wouldn't have to guess my sleep and wake up times.
Side request: if we can't have that, at least let us set different sleep times for the weekend. I work from 6 AM to 2 PM, so you can imagine the my sleep schedule is wildly different on the weekends.