It's not likely to be supported, mainly because we would be literally storing all request and response traffic for an API in our infrastructure, which would break all sorts of Privacy rules.
If you want to debug throughput on Hybrid, you might want to use a plugin such as this one:
Where you can offload inbound request data onto a queue for inspection. It won't record responses though.
It is also possible to enable a correlation ID, which you can inject into the header, if your APIs do any kind of logging, you could then use this ID to match your app logs to the requests stored and processed by the queue.