How was Kara channeling Alex?
So, first of all: Kara has a tendency to mimic the women she looks up to whenever she’s feeling uncomfortable in her own skin. Alex is her default, but sometimes it’s her mom or Eliza, or Astra, or Cat. Kara draws strength from others – and borrowing what she perceives as their strengths is how she copes with uncertainty/anxiety.
Second: the EPs were not lying when they said they were refocusing on the core elements of S1. There are multiple callbacks to the pilot episode in 3x01, and several with Kara & Alex in particular.
Winn sets up this parallel early in the episode with his line, “[Kara] went from being Little Miss Sunshine, to, well, Alex.”
We’re supposed to laugh, but we’re also supposed to recognize the truth in this. How am I sure? Because the narrative reinforces the point – J’onn not only tacitly agrees but also highlights how Alex’s “unrelenting seriousness” is a) not Kara’s normal behavior; but also b) how she’s behaving right now.
The story then runs with this for the front half of the episode. Kara’s entire demeanor is more reserved, as is her body language. Her voice is clipped and more commanding. She’s mission-focused to the point of being brusque with everyone around her. And she’s superheroing at a breakneck pace even though she doesn’t need to, as we heard in several background scenes, because she has it in her head that it’s the only way she’s still worthwhile.
Kara is acting like an unhappy,
passive-aggressive person with a work ethic that puts other overachievers to shame because she’s afraid there’s no worth in her humanity vs. superpowers.
In other words: Alex.