net: lib: http_server: Fix HTTP1 POST request handling

In previous batch of fixes it was overlooked that streams are
HTTP2-specific concept. While for HTTP2 we need to track headers reply
state for each individual stream, at HTTP1 level we need to track this
at the client level. Hence, reintroduce respective flags to track
headers reply state, but only for HTTP1.

Signed-off-by: Robert Lubos <robert.lubos@nordicsemi.no>