I don't want to diminish that by claiming to have all the answers, but I would suggest a few things.
Preface: My overall advice would include a complete overall to the status quo US approach to Israel and the middle east pre-10/7. The prior plan -- which was to help buy the support of all of Israel's neighbors to isolate Palestinians from any consideration was deeply immoral, inhumane, and as 10/7 showed us, strategically unsound. But for the sake of the thought exercise, I'll answer as if I supported Biden's overall objective, which is to maintain the apartheid regime under a veneer of plausible deniability that preceded 10/7.
First, Biden should've imposed a series of limits of Bibi from the start of the war. He should've privately laid out the objectives the US would support and the length of time available to conduct it, and "leaked" some of these discussions. He acknowledged the risk that Israel would overreach as the US did during 9/11 -- which by the way, HE himself bears great responsibility for. He was the ranked minority member of the Senate foreign relations committee in 2001. Antony Blinken was his main foreign policy advisor when he passed the Patriot Act, the Authorization for Use of Military Force that began the Global War on Terror, and the separate Authorization for Use of Force to invade Iraq in 2022. Considering all this, there was no reason to agree to give Israel a blank check for actions he publicly acknowledged were likely to create a disaster.
Second, he should've made clear during the first ceasefire in November of 2023 that the war was now over. They'd already killed tens of thousands of people and collapsed most of the infrastructure in Gaza. They'd made their point, and it was time to get the hostages home and negotiate a "day after" arrangement. Again, I would advocate for an actual long-term peace plan for Palestine, because the whole framework prior to the war assumes a permanent immiseration of Gaza that I do not support, but if that's what you want, this would've been a practical time to do that.
Third, there was always the problem that Netanyahu was trying to stay out of jail. He knew that if the first ceasefire held, it would mean that the war cabinet would dissolve, opposition leaders would call for elections and an investigation into the failures of 10/7, he'd lose office, face trial, and likely go to jail. Personally, again, I think this sounds very appropriate. But if you're Biden -- who genuinely thinks of Bibi as his little brother despite the fact that Bibi is a ruthless psychopath who would slit Biden's throat without hesitation -- you could offer to cover Bibi's ass by arranging for his complete pardon in exchange for peacefully ceding control.
Overall, this isn't really chess. It's more like a standard operating procedure. But truth be told, Biden did what he did because ultimately, this was all the outcome he wanted.
I know that sounds sick and deranged, but if you go through his entire career, it's always been there. From when he shocked Israeli Prime Minister Menachem Begin by justifying violence against civilians in a private meeting in 1982 to his repeated acts to undermine Obama in his dealings with Netanyahu, Biden has always been committed to a maximalist approach towards Palestinians. And now we're here.
This is how you know it's a proxy war.
As you point out, Biden's decisions were obviously ones that would prolong the war rather than affording a decisive counteroffensive. This was because the goal of slowly bleeding Russia's military out to weaken a rival power and bolster the American weapons manufactures was placed more highly than than trying to put Ukraine into a position of strength from which to demand a ceasefire on their own terms.
I don't know what Zelensky wanted, or what his plans were. But I think the most obvious and sensible approach would've been to privately lay out the bargain: the US gives Ukraine more or less everything that it wants to kick Russia's ass for a couple of months with the awareness that a full defeat of Russia by Ukraine is impossible, and pursuing a regime change would be inviting a nuclear world war. As such, the US goes hard, and puts Ukraine in a position to make the most modest concessions necessary to end the war in a way that lets Russia survive while having demonstrated that the overall approach was a disaster.
Could Putin decide to try again a few years later? Sure. Is it likely? And would that situation have been worse than what we're about to watch Trump and Putin do? Jesus Christ, not by a Texas mile.
Letting the war continue under any terms into Trump's presidency should've been viewed as the number-one all-time greatest military vulnerability to Ukraine, and should've been prevented at any cost.