test: add request body lifecycle tests for Copy as cURL (#10020)

* fix: show request body for pending requests in Network tab

The request body was hidden until the response completed, so the Request
tab and Copy as cURL omitted it for requests still awaiting a response.
Gate it on the request having been sent instead, and never cache or show
a body fetched while the request was still being sent.

* docs: link release note to #10020