Can I simultaneously get iMessage notifications on my Apple Watch series 6 and my iPhone?

I am a new to the watch. I expected that I would get all messages/email notifications on my watch as they came in regardless of whether phone was on or off - this is what would work best for me. I am frustrated that this isn't the way the system works or that it isn't an option for those who would choose it. Ah well. I appreciate the effort you made to educate me. Many thanks