How to auto-advance to NEXT message when deleting current message?

You are welcome.

In my Apple Mail configuration on Big Sur 11.6.3, and Monterey 12.2.1, as long as I have some Mail message selected, the viewing window is open on that message. When I backspace to delete a currently selected message, it advances to the next message and that is also displayed in the message viewing window.

If you are referring to Apple Mail, select the message that you want to delete, and press the backspace key. The message highlight will auto advance to the next message.