I’m afraid it’s not possible to use that for any sort of notifications, but if you’re after controlling what other users in your Marketing Cloud instance do with the data synchronization in Contact Builder, you have two options:
By far the most simple one - restricting their access to Contact Builder: https://help.salesforce.com/articleView?id=mc_cab_enable_contact_builder_access.htm
A lot more complicated, but in the end it would be possible to build a functionality used for sending email notifications: creating a data extension structure log.
The basis for this solution would be Gortoningron’s blog post about building an inventory of all data extensions in the account: https://gortonington.com/data-extension-inventory-for-your-sfmc-business-unit/
Instead of building an inventory of all Data Extensions in the account, it would be sufficient if you only retrieved information about the Synchronized Data Extensions and their structure.
You could log the number of columns in each of those and the column names. And by comparison to the previously logged values, you could set up a Triggered Send to send you an email notification that something changed.
This could be run on a daily or even hourly basis in Automation Studio.