Notes on Mac not syncing over iCloud, but does sync from iPhone to Mac

With the MacBook Pro running Monterey 12.8 and iPhone 16.0.2, entering notes on the Note app don't appear on the iPhone.

However, notes entered on the iPhone promptly appear on the MacBook.

But... If I enter something on the Notes app, and it doesn't appear on the iPhone, if I enter something else on the iPhone and hit "Done", bam, the info entered on the MacBook appears.

It's as if the Notes app isn't initiating a save to iCloud unless it receives a query from the iPhone. Clearly a bug, but looking for a workaround. I'm waiting on updating to Ventura due to a software limitation of an important app that's not yet compatible. Maybe updating the iPhone to 16.2 could help, but haven't tried.