I can think of two different ways to do this:
1) Script
You could iterate through all of your applications and tables using API_GrantedDBs and for each perform a query that will return or count those records created in the last week. What query you perform depends on the state of your applications as you may not have a known apptoken to use against all applications. Also this process could generate a lot of API calls which could be expensive if it ran too frequently, take long time or even grind your browser to a halt.
2) Service Worker
You could also implement a Service Worker that silently monitored every network request and counted or logged all requests of a particular type. This approach could only work for Chrome, Firefox, and Opera browsers as we are waiting for Service Workers to land in Edge and Safari.
