May I know how to active apple watch silence mode when iPhone active?

I was awaked by apple watch notification rings last night either I actived sleep focus and silence my phone. I don't know why my outlook can send watch notificaion although none Apps in sleep focus allow notifications list. I enabled Share Across Devices so my watch was in sleep focus at that time. I also notice I can add Silent Mode in Focus Filters in sleep focus, but there is no setting for apple watch auto active Silent Mode when sleep focus active.