But what you are saying doesn't match much the data (at least in Italy). In Italy females consistently get higher grades than miles, in all levels of school, and they do that from other women teachers (including STEM subjects).

How this matches "being held to a different standard", for example?

They are the vast majority of schools in humanities (languages, classical studies, etc.) and all "licei" (=high schools created with the purpose of forming the ruling class back in 1920s) and they are the minority only in technical schools (which are generally lower quality schools more oriented toward professions than university) and in the scientific high school.

This also doesn't seem to suggest any encouragement or discouragement in one direction or another, BUT it does match perfectly the culturally rigid gender stereotypes about women being more creative and fitting roles of care.

Also worth noting that women attend university in a higher % (56%) compared to men (also a result of gender stereotypes IMHO) and with higher grades on average. They are also the majority of PhD students (59%).

So my question I guess would be: why medicine and psychology are mostly and overwhelmingly women faculties, while engineering etc. are the opposite?

any interest or persuasion being dismantled and/or dismissed for decades before uni.

I wouldn't say "any", but I would absolutely say that interests in fields that are traditionally male-dominated are discouraged for women and viceversa (I have written in another comment, the imbalance in educational science is even higher than the one in engineering).

So I do see gender roles, I do see cultural influences about what is " for men" and "for women", I don't see the different standard women are held up to.