Can I get notifications on my Apple Watch and iPhone at the same time?

I want both my watch and my phone to make a noise whenever I receive a message while still using wrist detection. Is this possible?

Since getting my watch, I miss notifications constantly. My watch is quiet or it's often not on my wrist, but yet still close by. Then I pick up my phone and there's a whole list of messages from hours ago that I missed. This is very disruptive.

If I understand correctly, when my iPhone is locked and in bluetooth range of my watch, then notifications will only go to my watch. But if my phone is unlocked, then notifications will only go to my phone? Is this true? Please, tell me it's not true. Please tell me that the user-friendly, Apple ecosystem will allow me to personalize the way I want to receive notifications across all my devices.

Is there any way I can adjust this? I've read the posts that tell me to turn wrist detection off, but I don't want to do that. I also have been told to turn my watch notifications off, but I don't want to do that.

I want to be able to use all the features of my watch and wear it all the time and have it connected to my phone and have my phone make a noise or vibrate every time I get a message (unless the phone's on do not disturb or airplane mode of course)