The "pick me" label as its applied to cis women is a misogynist concept used as a way to drive a wedge between women. Just as general advice from an ally, it's probably not advisable to onboard kind of short-hand into trans communities.

Internalized misogyny takes a lot of forms, it could manifest as "pick me" behavior, but it could just as easily manifest as an obsession with hyper-sexualized misogynist anime characters etc.

The goal should be to help other women work through and get out from under internalized misogyny, not label, police and condemn them for it.

Putting down other women is carrying water for misogynists, whether it's criticizing them for being too femme or for being tom boyish or whatever other characteristics are "bad ways to be a woman".

As I_dont_want_to points out; these kinds of labels are easily misapplied and weaponized. Better to just criticize the specific negative behavior itself than label the person as something. In the same way that calling a person "a racist" is less productive than pointing out that they're "being racist". One is aimed at the nature of the person, the other addresses behaviour.