net: lib: http_server: Clear http1_headers_sent flag on new request

http1_headers_sent flag has to be cleared when entering
HTTP_SERVER_REQUEST_STATE and not only on the client init. Otherwise,
serving multiple HTTP1 POST requests over the same connection does not
work as intended (headers were not sent for the second and further
requests).

Signed-off-by: Robert Lubos <robert.lubos@nordicsemi.no>
(cherry picked from commit 086faa56)