This is difficult to answer from anything like official sources, as to the [true] long-term planning of the current administration. Given the election cycles in the US, perhaps no such planning can even exist.
For the rest, there's speculation and political accusations--lots of the latter, in fact. There are certainly those US-side who argue that the US hasn't been doing enough to help Ukraine win faster, and that thus the US is prolonging the war (intentionally or not). And those who even claim that the current administration is using/prolonging the war as a distraction:
But Biden officials adamantly reject the proxy label, noting that it is a defensive war Ukraine didn’t start and that Kyiv is fighting for its very survival. [...]
Donald Trump, in a recent presidential campaign video, called the war a “proxy battle” and said the Biden administration was only “pretending to fight for freedom.” Instead, he said, Biden “globalists” were using it to distract Americans “from the havoc they’re creating right here at home.” [...]
While some conservatives slam what House Speaker Kevin McCarthy (R-Calif.) has called Biden’s “blank check” for Ukraine, others think the president has been too restrained in doling out enough aid for Ukraine to defeat the Russians. “If you want to fight a proxy war against Vladimir Putin’s vindictive, brutal, destructive desire to be remembered as Peter the Great, then fight the damn proxy war; don’t do it halfway,” the National Review’s Jim Geraghty wrote last month.
Anyhow, the best you can learn from the Biden administration are same rather vague statements like:
The administration itself has provided rhetorical grist for Putin’s proxy portrayal. “We want to see Russia weakened” so that it can never invade another country again, Austin said early in the conflict.
At a NATO summit in Madrid last June, Biden said Americans should be prepared to pay higher energy and gasoline prices “for as long as it takes” to defeat Russia, a phrase he has subsequently used in nearly every statement since then about Western aid for Ukraine.
“Ukraine will never be a victory for Russia. Never,” Biden said as he marked the anniversary of the war’s beginning during a visit in February to Kyiv.
But in more practical terms, the US seems to be "tailgating" so to speak, i.e. only making rather short term decisions.
Asked what happens if Ukraine doesn’t succeed in pushing back Russian front lines and reclaiming significant territory, the Pentagon’s top official deflected.
They are always “looking further down the road,” Austin said. But “we want to make sure that they’re successful in this next fight. I think if you lose focus on that, some of the other stuff doesn’t matter.”
According to a Defense Intelligence Agency assessment among the leaked documents, “Negotiations to end the conflict are unlikely during 2023.”
So that kinda seems to be the horizon that US administration is working on.
Thus, there are those who say that the US is unintentionally prolonging the war:
The United States is pursuing a ‘gradualist’ policy in Ukraine, ratcheting up the pressure on the Russian invaders by progressively arming the Ukrainian military. Gradualism didn’t work in Vietnam, and it may not work in Ukraine.
In the 1960s, President Lyndon Johnson feared that the war in Southeast Asia might escalate out of control. He worried Moscow would threaten Berlin and that the People’s Republic of China might enter Vietnam with massive ground formations like it did in Korea.
Johnson tried to calibrate the American use of force in Vietnam to send nuanced “messages” of American resolve to the leaders in Beijing and Moscow. [...]
Today, despite repeated pleas from Ukrainian President Volodymyr Zelenskyy for combat aircraft, U.S. President Biden insists that Zelenskyy “doesn’t need” F-16s. National Security Advisor Jake Sullivan has reinforced the president’s position, indicating that the Biden Administration is carefully measuring Ukraine’s tactical needs on a case-by-case basis. In a classic example of gradualism, Sullivan did not rule out providing Ukraine with F-16s at some later date.
Absent a coherent strategic framework for resolving the conflict, it’s tempting for the Biden Administration to focus on Ukraine’s needs on a week-to-week or a month-to-month basis. That tactical, short-term focus is prolonging the war.
That's probably as good of a conclusion are you're likely to get on this, given the know/revealed facts. That article also concedes that "The Biden administration’s concerns about escalation are legitimate." But argues that that is ultimately a mistake.
I don't fully share the ultimate conclusion of that author. While one can bring up Vietnam as to why gradualism can fail, the US help to the mujahideen against the USSR was successful (but only in the sense of driving out the Soviets, with little regard for what happened afterwards in Afghanistan). That US engagement was in fact executed with the idea of keeping the pot boiling without overflowing. (However, in that case, that strategy was also dictated by the Pakistani government, which served as the primary conduit of proxy aid. In fact, that pot analogy was Ayub Khan's words.)
As for the war in Ukraine, one can point to some geopolitical advantages that have accrued to the US, like Finland joining NATO (and some increased LNG sales), but until the US archives on this are opened (some 25+ years from now) or administration officials decide to write about that in their memoirs, it's hard to say how much they've considered those a primary goal in their war-related decisions.
There is the flip side that Russia gets more dependent on China, which is something that at least some EU leaders have openly worried about, and which also worries the US public.