This article mentions that the iCloud passwords stay local when you turn off the synchronization. I just tried it on my Mac and the Passwords app did keep my passwords.
Now I've always had my passwords synched with iCloud. So, to go back to your original question, I'm not sure why your passwords were not migrated. I would have expected the iCloud keychain to move from the Keychain Access app to the Passwords app. When I look at my own Keychain Access, I still see the iCloud Keychain in the sidebar but it is empty.
You are right to be concerned about the Keychain Access app. Apple removed the secure notes functionality from the Keychain Access app when they introduced the Passwords app. (I know it's odd since passwords and secure notes are not related.)
Now this is what I would try to get the passwords on your M4 Mac: on your 2015 MacBook Air, turn on the passwords synchronization, do the same on your M4 Mac. Wait for the Passwords app on your M4 to show your passwords and then turn off the iCloud password synchronization on both devices.