Hi sc2!
It doesn't seem like there is any function that logs the date and time of changes made to the note field of a specific client device. I use a text expander software that replaces a given shortcut phrase (like /date) with the current date and time, which makes the function available system-wide too.
We would recommend that you leave this as a feedback suggestion for the product team via the Meraki dashboard Give your feedback function, so the product team can look into the possibility of adding it in future dashboard updates.