So the negotiation is by Israel, not by Qatar, Qatar only doing the mediator part. So why would they keep this off the public?

Also why IDF always demand something impossible when they have the power? First they demand the evacuation of 2 million toward south in 24 hours. Now they sabotage the communication, keeping the airstrike, but demand the hostage to be released in just a few hours. They also know there's multiple faction fighting together and might not be cooperative, which is another info that's off-public.