Trump believes that strongmen are entitled to everything they can manage to steal.
Sure, but in Trump's fantasy, he's the strongman.
Trump has an extremely narrow view of the world: it's winners and losers, and a crude balance sheet. For Ukraine he sees the numbers for the USA in red. Stuff like values, democracy, allies, wider geopolitics, international order, sanctity of sovereignty and borders etc. none of that matters. He sees the USA spending money to help a vulnerable country when the USA could mug it for profit instead, and that makes no sense to him.
So extort Ukraine and turn the numbers in the accounts black. I think Trump's admiration for Putin is a factor, as is that Trump is cruel and bullying and likes kicking sand in the face of weaker people, and that he would narcissistically like to posture as dealmaker and peacemaker. But mostly he just wants to extract and extort wealth, and Ukraine is the only country he can extort here, so he will. If he gets a "peace" and then Putin continues invading it's okay. Sure, he'll not get all those minerals he wanted, but the USA is no longer spending money either so it's no biggie. He'll send a ragey few messages Vlad's way for form's sake and do nothing at all.
More to the point, I think this is all sort of happening anyway. I think the peace deal will fail and Trump will likely walk away completely, achieving the aim of removing the cost from the USA. This is a de facto win for Putin, but Trump won't care. I think Putin knows this, which is why he's fucking around with Ukraine and Trump: he knows the USA is out and gone and he's just waiting, playing along until that happens.