Phone notifications going to apple watch

My phone notifications keep going to my apple watch, even when my watch is actively charging and should not be receiving notifications. Since it activates my watch, I don't get notifications on my phone when I get messages. My watch is fully attached to the magnetic charging cable and I see that it is charging on the lock screen. Is there a way I can stop notifications from going to my watch while it is charging?

If it helps, I have a series 5 watch with software version 8.1 downloaded. Thank you for your help.