You could do this with a Service Worker but I think there would be more than three cases to decode. Basically the Service Worker would monitor network traffic and if it sees for example an ?a=er it would modify the network request to include an extra field indicating a form was used. Likewise, if ?act=API_* was seen it would modify the network request to include the extra field indicating an API was used. Similar arrangement for Grid Edit.
You would need to cover both GET and POST requests slightly differently and to be comprehensive you might want to record with imports separately.
The main challenge would be to discover and cover all the edge cases.
