[Http]: Correctly handle request bodies when resending with authentication.

My previous changes modified the way how we're handing the request body when
resending a request due to a 30x redirection.

Authentication is a "special" form of redirection because we sometimes need
to resend a request with additional authentication headers.  Unfortunately,
I forgot this, causing a regression which is now fixed.

This has been reported as bugs #19119 and #19068.