notes "ON my Phone" did not transfer to iCloud

The notes in the iCloud folder are not backed up but synched between your devices. You'll see them on any other device including your new iPhone.

The notes in the "On My iPhone" folder are backed up along your other data not synched in iCloud. Restoring an iCloud backup on a new device would restore those notes.

This being said, if your backup is done as a precaution, use the Quick Start functionality to transfer all your data from the iPhone 10 to the iPhone 15 Pro. This is the easiest way to set up a new iPhone: Use Quick Start to transfer data to a new iPhone or iPad - Apple Support.

NikonZ8shooter wrote:

I have spent over 4 hours today trying to upload / backup my iPhone 10 to my iCloud account. Mostly successful and my notes that are listed as iCloud transferred, but not the notes listed under "On My Phone"

Any suggestions on how to fully back up ALL data on my old phone before I try transferring to my brand new iPhone 15 Pro

You have to manually move the notes from "on my phone" to icloud within the notes app, then the notes will sync to icloud, not backup.