Apple iphone and apple watch
How do I get my apple watch to function when my iphone is plugged into the charging port?
Question marked as
Yes, that helped. The reason you don't get notified on your watch in the scenario you described, is because your iPhone screen is open (active) when the message arrived. The way notifications are designed to work is if your iPhone screen is active, notifications arrive at your iPhone. If your iPhone screen is locked, notifications come to your Apple Watch. This is by design and how Apple intended it to work.
See this and note the statement at the top which says Notifications come to your iPhone or your Apple Watch, but not both --> Notifications on your Apple Watch - Apple Support