keychain access syncing icloud keychain problem, Big Sur vs. Monterrey

I have a late 2013 macbookpro running Big Sur 11.6.5 and a 2020 desktop that I recently upgraded to Monterrey 12.3.1. I have "Keychain" enabled under "iCloud" settings on both. When I upgraded the desktop computer to Monterrey, I noticed that my keychains looked different in "Keychain Access". On the laptop running Big Sur I have (and previously on the desktop, I had) two "Default Keychains": "login" and "iCloud". Now, on the desktop, post-upgrade, I have "login" and "Local Items". The "Local Items" keychain seemed to contain all of the items that were previously under the "iCloud" keychain. However, it doesn't seem to be updating, when I add items to the keychain labelled "iCloud" in Keychain Access on my old laptop. Nor does the laptop update when I add a password to the iCloud keychain in Keychain Access on my desktop. Formerly, the iCloud keychain would by sync between computers. That was the point of having an iCloud keychain in Keychain Access, I thought – to have one repository for passwords and secure notes across different computers. I'm not sure if something's gone wrong in my upgrade to Monterrey, or if the system has changed, and I'm not understanding something. If my passwords are no longer syncing, that's a problem, especially if my old computer were to die.

I'm also not fully clear on how Keychain Access is meant to integrate with the new "Passwords" System Preference. I think that the Passwords system preference applies only to website passwords, implying that Secure Notes aren't available via the Passwords system preference. Similarly, if I create a password item in my "iCloud" keychain in Keychain Access, it won't appear in the Passwords system preference (though if I understand correctly, all Passwords in the System Preferences pane will appear in Keychain Access). As a result, when I only have my iPad, I don't have access to many important passwords – just the ones tied to websites. And not my secure notes either. Right? I suppose the idea is that any password item created directly in Keychain Access will have to be used at some point on some website, and then the system will ask me if I want to save that password – in the Passwords system preference, that is, not in Keychain Access, where it is already saved, and now will be doubly saved.

To sum up:

1. Why is my iCloud keychain now named "local items", after transition to Monterrey on the desktop?
2. Why is "local items" not syncing with my iCloud keychain under Big Sur on the laptop?
3. Does my second paragraph capture how the two password systems are meant to work together?

Thanks in advance for any suggestions.