It’s really not that complicated: Bennet allied with Lapid, making it impossible for Netanyahu to form a coalition including the Chareidim. Case closed.
You missed the point why did Bennet feel he could make an alliance with Lapid instead of the charedi parties without destroying his own party. In Israel MK’s can leave their party and join other parties or their own party , It happens all the time.
It seems the Dati Leumi in israel would rather be with Chilonim than Charedim. HONESTLY ask yourself why. Saying they are Goyim and Hate torah is not truthful, The Dati Leumi are religious