net: lib: coap_client: Use reset_internal_request() instead of flagging

It is error prone to flag separate booleans, so try to use
reset_internal_request() every time we release the internal request
structure.

Also refactor the reset_internal_request() so that we reset the
timeout value so it does not trigger again.

Signed-off-by: Seppo Takalo <seppo.takalo@nordicsemi.no>