I feel this would be a custom solution...
I know there is a "Data Insertion" API (I've not used it)... but in theory, if you are using APIs through a tool (and not just making calls directly with the API), you could probably create a Data Insertion API call to track the usage in conjunction with the API being "used"??
This would take some planning, testing, making a POC, etc to see if you can get it working...
The other thing you should check is IF the API usage shows up in the Admin Logs... I don't have a lot of APIs in use right now, so I can't really check my logs... but this type of usage may already be reported (not in the suite itself, and using your server calls bandwidth), but part of the Admin monitoring functions that you can see what people are using and when....