Note this is note a post in who is right or wrong on the Israel and Frankensteinian war there are a million threads to debate that.
This is about what is Israelis best strategy.
They need to learn from 1967! They know Hezbollah is going to attack so don’t wait. Make ir appear that they will invade Gaza and then preemptively strike Hezbollah in Lebanon with everything you have! Make it swift, decise, and devastating! Do not care about collateral damage! That should impact the strategy one bit. Do not warn them one bit. Rain hell about them and then invade in a blitz creed style destroying everyone and everything in their way.
Once Hezbollah is neutralized, hit Gaza with a sledge hammer and reestablish control.