In Doctor Strange in the Multiverse of Madness (2022), America Chavez and Doctor Strange landed on Earth-838 by traveling through the multiverse, and Doctor Strange asked her to open a portal to return back:
Doctor Strange: Wong is back there alone with Wanda, and I'm the only hope he has.
America Chavez: I can't control my powers...
Doctor Strange: You must be able to control it somehow. Even I could...Sorry.
Why did Dr. Strange apologize to America Chavez here?
It's subjective, but I think Strange apologised to America there because, as he spoke this line specifically....
You must be able to control it somehow. Even I could...
... he was beginning to get frustrated (out of concern for Wong's safety) and raise his voice towards her. Before he completed that last sentence, he noticed her take a step back away from him, with a concerned look on her face, suggesting that his demeanour in that moment was frightening her a little bit.
Strange was aware that a variant of his had tried to kill her not too long before, and as such, she had good reason to be concerned by the frustration he was expressing towards her there. Realising that, he checked himself and apologised, in order to reassure her that she had nothing to fear from him.
Personally, I don't think he genuinely considered hurting or killing her in that scene, but all the same, he felt it appropriate to apologise for inadvertently behaving in a manner that could give her that impression.
Because that's the line of thinking that the other Strange went down, causing him to attempt to kill her in order to take her powers and control them.
He's apologising for considering it, after promising he wouldn't.
