Don't worry, I'm not afraid of saying it!
Transwomen DO have male privilege, and that is NOT something that they can transition out of since, you know, they will ALWAYS be male. Male socialisation is also a thing, but you're conflating it with male privilege, though they are related.
Male privilege refers to the benefits and advantages that males get just because they're male. For example, Ethel Cain is adored because he's a TIM, despite being openly racist, misogynistic, into incest, etc. No one would ever be that lenient for a woman.
Male socialisation refers to the way males are taught by family, society, media, friends, etc, to behave and think as males.
Neither of these things magically vanish just because a male claims to be a woman, no matter how well he "passes," or how much this FACT upsets you, a male.