I am eager to see her review of "Bring Him Home." I said, "Kurt sang high." She briefly touched on that, and said that it was "+three semitones higher than the original" (whatever semitones are) so Rachel could sing in that key too. The plot was that Rachel was being "a nightmare," and Kurt said he was the only one who could take her down. He knew how to challenge her, and he planned it very carefully. The thing is, Kurt is Rachel's best friend, but Blaine is Kurt's best friend. Also, Kurt now has Adam, who he's friendly or more with. Kurt doesn't need emotional support from Rachel, not that he was getting it. Kurt doesn't actually need emotional support from anyone, though he needed it from Burt before he moved to New York. He had emotional support from various people to various levels before he moved to New York.
Rachel is the one who needs support and affirmation. Kurt could have lived without it. Like when he first got into NYADA, he was quietly practicing in beginners' dance class when Adam came in and complimented him on his plie. It was a huge contrast against Rachel's battles with Cassandra. Rachel felt entitled and like she was more skilled than she was. Kurt accepted that he had things to learn, and is going about learning them, and in two separate episodes it was established that he got no support from Rachel in learning the ropes there. It was just as well, considering how she acted.
Meanwhile, back in Lima, in "Diva," Blaine said that Tina was the person he felt closest to in school. It's an important specification. Kurt is Blaine's best friend. Blaine has Sam as a friend, and Blaine is one of the bros. Blaine doesn't feel like he has emotional support at home, but he has it from Kurt and from friends at school. Blaine's still damaged, as are all the kids formerly and currently in New Directions, but he's doing better.
Kurt adjusted to living in New York, and adjusted to going to NYADA. He did his research, he worked hard, and he made plans. Kurt is used to having to work harder just to get a chance, and having to be better than others to be accepted. In some ways, Blaine also has to be better than others to be accepted, and, like Kurt, he is painfully aware of it. They just cope with that differently, and Blaine is more willing to compromise about it. They have different kinds of survival skills.
So Kurt's choosing his battles, quietly learning what he needs to learn, and getting long-distance emotional support from Blaine and Burt, and local emotional support from Adam. Isabelle's likely still around, too, as Kurt said he'd keep interning at Vogue part-time if he got into NYADA, and we haven't heard otherwise.
Rachel probably hasn't actually learned anything, which may come back to bite her at some point. Kurt is earning respect.