I know the media always refers to the people living there as Russian-backed separatists but they are in fact Ukrainians.

Force-recruited to fight on frontlines with Mosin Nagants or, alternatively, Wagner green men.

So why hasn’t the US sent 200-300 tanks?

Because they're chicken and don't understand Russia. Russia sees such hesitance as weakness and reason to continue on, as evidence that the US isn't really in it for the long run. And, I mean, they're not wrong in that regard proper commitment looks quite differently.

Why did the US demand that Ukraine launch a counteroffensive with insufficient tanks and air support?

When did the US demand such a thing? Ukraine has plenty of reason and grit and will to decide that on their own. Oh and there's a suitable number of tanks for what Ukraine is doing (they're not stupid and don't overcommit), the issue indeed is lack of air superiority, all that fancy NATO hardware is supposed to be used with NATO doctrine which involves throwing air superiority at the enemy until the ground frontline is the enemy's whole territory. But Ukraine is making the best out of the situation and picking off positions NATO would pick off from the air with various artillery systems, both medium and long range. And they're very good at it, which shouldn't really surprise anyone as that's good ole soviet doctrine and Ukraine always was the core force in the red army anyways.

Why is the US trickling in just enough equipment to prolong the conflict as much as possible without giving Ukraine everything it could possibly need to win.

Because they're a bunch of chickens who don't understand Russia. Alternatively, with some conspiratorial thinking, they want to prolong the war -- I frankly doubt it, never attribute to malice what can be explained by stupidity. But that's irrelevant, in any case: Because that should be reason for you to demand that more weapons be shipped, not less.

Why is US propaganda so different from the actions the US is actually taking?

I wouldn't know I don't follow US media way too much of a partisan clown show anyway.