I think what a lot of us are trying to get across here is that socialisation of both sexes (which has ultimately led to a grossly low number of female STEM workers) is heavily based on sex and NOT gender, so 'identifying as a woman' (which IS down to gender unless you're born a woman) doesn't rectify the problem.
I'm going to suspend my belief system for a moment and pretend gender isn't a bullshit concept.
My gender is individual to me, and very personal to me. Only I can know it, only I have access to those feelings. Same as every other person on the planet. The very concept of gender relies heavily on self-identification. How I see me. However, until one decide to wear their gender on their sleeve so to speak, how others see them, is heavily influenced by their sex.
The vast majority of people who identify as gender 'that doesn't conform to their biological sex' - trans, non-binary etc - do not recgonise this until, at the earliest, adolescence. Some de-transition (or accept they are a butch female or effeminate male), some don't.
When they do start to wear their gender on their sleeve, they will most likely experience a different kind of socialisation. However, as someone pointed out before, people treat others based on their sex from the very early days, even holding newborns differently according to sex. Any parent will tell you that, come toddlerhood, socialisation based on sex is well ingrained (especially now in the world of pinkification). The presents you're bought, the way you're expected to behave, the clothes available to buy, what is marketed at you. Even if a person identifies as a different gender to that of their sex from adolscence (teenage years), very little can be done to undo the decade and a half long socialisation. It's not like one day someone says "I am now a woman", people forget that you were ever a male, and retrospectively adjust their attitude and behaviour towards you.
Even when someone does announce their gender, eg as a transwoman, they will not be socialised from there on in as a woman. They will be socialised as a transwoman.
I hate to waffle but my point is that this scholarship SHOULD be given on the basis of sex, because that's precisely why women have been held back for so long. Whilst gender will prompt a new form of socialisation, it won't even begin to scratch the surface of borne socialisation from sex. If gender was not a concept, and trans did not exist, you would still have the same inequalities from male and female in STEM field. In brief, gender has bugger all to do with it, and a scholarship for women should not take gender into account