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Look at their history as a culture. They don't usually kill their own. Fuck, to this day they're still defending the corpse of rapist/murderer leo frank.

They were initially paralyzed by the reports of hostages. They don't give a flying fuck about anyone else, but they are absolutely dead set on not losing any of there own.

Letting hamas do it would be uncharacteristic in light of these details.

However, lets examine some things:

They have a history of attempting to project invincibility. In a vulnerable position after an attack, they could and would spread rumors of how israel itself plotted the entire thing. The premise is if uncertainty is increased regionally, other nations that are neutral or hostile are less likely to join in the attack. This says, contrary to the mask of invulnerability, israel is in fact afraid it is going to have its neighbors pile on to the war on the palestinian side.
This would also explain the u.s. sending war ships in great number, its genuine deterrence. In that light, rumors about another u.s.s. liberty could either be spread by the u.s. itself, or by hamas and company. What did the u.s. do in ukraine? Attempt to antagonize russia into actionable attacks that would cause the world to condemn it, and justify the sanctions in place. Failed of course but I digress. This is the u.s. playing at strength. This suggests the 'u.s.s. libery 2' rumors being spread are likely pro-palestinian nations or groups, sending a message to the u.s.: that they can fuck up our domestic relations with israel, and force another front to be launched in the middle east and the russia-ukraine war, during a critical time in the u.s. where american support for the regime hangs by a thread.

Speculating, the pull back of IDF troops could be two things: false information to feed the fog of war narrative, or a rift.
We know netanyahu faced mass riots, maybe even abortive color revolutions. The first assumption would be he pulled the border guards back, to bolster his own position. Another take is that factions unsatisfied with him want to create a scenario where the IDF is forced to decide if netanyahu is capable of protecting and leading israel. Sort of like a spat between him his opposition.
The polarization that made netanyahu indepnsible (turned into the glue of the coalition government) would then be dissolved by the need for a unified front to face the external threat.

The balance of power then shifts away from benjamin and his opposition now working together, to the only other leader: the head of the military, gallant.

If I'm correct we will shortly see an outcry of anti-BN rioting the moment a lull in the fighting hits, and calls for the military to take over 'temporarily' in israel.