If Israel doesn’t cause the elimination of Hamas then this will be seen as weakness. Hezbolla has 100k missiles, if they get involved then that would mean 10’sK Israeli casualties per day. This might cause Israel to unleash the airforce and maybe go nuclear.
One day that whole area will go nuclear
If it’s an existential crisis for Israel they would most certainly threaten to drop a tactical nuke on Hezbollah.. with willingness to follow up.