Israel actually didn't do that - Netanyahu literally said "this is not another skirmish, this is a war" and gave explicit goals to the war (bringing back the hostages and dismantling Hamas). Later on an additional goal was added - allowing the return of Israeli internal refugees to their homes in the North.

Yeah, but that is for "internal consumption" and it doesn't affect any international relations, unlike "declaring war".

An interesting example is the U.S. which has been in a "state of war" (official term is "period of hostility") since 2001, a.k.a. "War on Terrorism" — and it still is! Which, by the way, gives a nice bonus of immediate citizenship for signing up for the military, without the need to wait for 5 years.