[Update]
Below is how I "resolved" this issue - this is definitely not a solution for most users. Before beginning, make sure to back up any notes that have been added/modified on your Mac since the syncing stopped working. Furthermore, make sure you have a time machine backup
Steps:
1) Delete the in-note video from the note that seemed to cause the whole issue
2) Ensure you have a backup of ~/Library/Group Containers/group.com.apple.notes , either via copy/paste to a temporary location or Time Machine etc
3) Turn off iCloud notes syncing via Mac iCloud Preferences Pane. This deletes all the iCloud notes on the Mac, *including* any you have created since the syncing issue began (hence my warning about backing things up)
4) Turn iCloud notes syncing back on - wait for the notes to download from iCloud
5) Using the backup from step 2, restore ~/Library/Group Containers/group.com.apple.notes to get the notes that were lost in step 3
Good luck