net: lwm2m: Remove handle_separate_response flag

It shouldn't be optional to handle separate response, as it's a
mandatory requirement according to the RFC7252:

"The protocol leaves the decision whether to
 piggyback a response or not (i.e., send a separate response) to
 the server.  The client MUST be prepared to receive either."

Therefore, remove the flag as separate responses are handled now
properly.

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