I don't think they know what they want

What would YOU want if you were a military leader of Israel there? (NOT a political one, just a soldier)

I think that they want exactly that. A military goal, not a political one.

For example "kill everybody there who takes a weapon and aims it at Israel, and then take this weapon away from his corpse."

They control the borders and they are systematically destroying infrastructure while stealing the land to be ‘settled’ by right wing Israelis. (They done let liberal folk become settlers.)

The right wingers have no issue with being bad neighbors or otherwise murdering Palestinians. And they are backed up by the military. Any resistance is returned 10-fold, with an associated grab for land.

If a cease fire can be forged, the control of the border will mean that the they will continue their existing blockade on imports of building materials such as cement, so new infrastructure cannot be built. They are even using construction equipment to remove or bury rubble, so it cannot be repurposed/recycled.

The plan is to do to Gaza what they have already done to the West Bank. Turn it into fragmented enclaves that lack access to basic resources. It’s clear they even want to block total access to the beach, to prevent fishing for food. It’s why they are literally selling the land that is currently being bombed. They want to make it impossible to live there if you’re Palestinian. They want everyone that isn’t part of their theocracy to die off, or emigrate.

Not related, but totally related.
I’ve watched these interviews with white supremacists in the U.S. who talk/fantasize about the creation of a ‘white’ ethnostate. They always talk about how there will be a nonviolent transition to this, saying that people who don’t match their racial parameters will be relocated to places outside of the state, or those who won’t have children will be allowed to live out their lives, etc. And that’s widely regarded with a ‘sure buddy’ and you know they’re full of crap. People don’t want to move away from their homes. They don’t want to go where they don’t know anyone. They don’t want to lose their jobs, their savings, all their stuff, the land they own and the effort they’ve pored into their home and land or the resources their home/land offers them.

But the situation in Palestine is literally that. People are ‘voluntarily’ relocating (after their homes, jobs, neighborhoods, and often, families) have been blown up by bombs. Or they’re staying and living out the rest of their lives - until they’re shot or a bomb goes off, or they die from malnutrition, thirst, or contaminated water. Hm.
I suppose it’s (relatively) nonviolent to the aggressor.

They've already invaded Lebanon before and every time it was for the same reason, and that was to prevent the Hezbollah terrorists from committing terrorist attacks against Israel. This time is no different

It's been clear and consistent since day 1 of the war. Israel wants the return of the hostages taken on Oct 7, the removal of Hamas from power, and the inability for Hamas or any other group to repeat a deadly attack within Israel.

That was the goal on Oct 7, that's still the goal. Anything else is just politics and propaganda.

Now, how effectively they have done so, and the methods they've employed are another discussion entirely.