Wa alaykum assalam,
By the night when it covers, and by the day when it appears, and by He who created the male and female: Surely, your efforts are diverse. (92:1-4
Will try to answer this question in a few stages.
1. We are all from Adam, and Adam is from dust. The base identity of every person is that he or she is a creation and servant of God. Regardless of one's sex, race, or even religious beliefs, all humans are created to manifest the glory of God. The Quran and hadith often refer to all human beings as `ibad (servants), all of which abide by His will (30:26). The natural intuition of the human being is submission to Allah - it is what the `aql inclines towards. Indeed all of creation is a sign of Him, and all of creation worships Him. Humans have been given a will, and with that will, a human can either reach his natural telos by developing his intellect, mastering language, and representing God; or by giving into ignorance and base appetites. In this sense, man is both celestial and earthly, spiritual and natural. All humans have a common, meek, worldly state, but the goal is to humbly ascend back to God.
2. Sex and gender are different. Sex refers to one's biological anatomy, while gender refers to one's social identity. The two are interconnected and do not vary independently, but it's important to make the distinction. Before the 1960s, gender was mainly a grammatical term used to describe words and inanimate objects - most languages have masculine and feminine tenses, and gender was not really used to describe people. Later, gender was used to describe the socially-constructed identities and behaviours associated with manhood and womanhood. So men as a gender had "masculine traits" (strong, independent, hard-working, etc.), and women had "feminine traits" (nurturing, emotional, etc.) Similarly, individuals would mix and match these traits, saying that they were male with some effeminate qualities or interests, or females with masculine qualities or interests. With the idea of gender fluidity, some feminists and LGBT activists began claiming that gender, which is largely social, can change willingly or unwillingly, and so one can be anatomically male but have a female gender, or be anatomically female and have a male gender.
3. Islam is, generally, sexually dimorphic. This means that there is an explicit recognition of two sexes. The Quran speaks of the male and female, believing men and believing women, and in some cases, different laws and guidelines are given to the two sexes. The implication is that, the two sexes are equal but different - both are human, both are servants, both have free will, both are capable of the highest good and the lowest evil, but due to their biological, psychological, physiological, anatomical, chemical, and social differences, there are some legal differences between the two. Our sex is not our essential identity, it is [philosophically] an accidental quality, and so the dimorphic laws that exist are not there to put one sex above the other, but rather they are there for our own worldly interests. In one narration, Imam ar-Rida (as) was asked why women inherit less than men, and his reply was that women receive a mahr, and a husband's wealth is distributed to his family. So inherent in his reply is some principle of equity.
4. As Muslims, we should probably ignore most of the debates on "gender". There is currently an obsession and fixation on the 70+ genders, "masculine" women, "effeminate" men, non-binary people, transsexuals, gender neutrality, what aspects of gender are socially-constructed and what aspects are biological, etc. Some of this is a pushback against the Victorian era's very elaborate version of what a male is and what a female is. The logical conclusion of all of this is to put gender aside. What is solid much more solid than gender is sex, which has a chromosomal basis - 99.98% of people are sexually dimorphic, and the exceptional mutations are not a "spectrum". The Imams of Ahl al-Bayt (as) have even given guidance on those few people who are born with both sexual organs - they have said that the working/functional genital is the sex of the baby; and so the other genital can be discarded or ignored. What is even more essential than sex is specie, and what is even more essential than specie is our status as a creation.
5. By putting gender aside, it does not mean that sex does not exist. Western Liberal Individualism makes the individual the basic agent of society. Their abstract of the philosophical individual is basically an androgynous, raceless, religionless, ageless blank person, who should be given as much freedom and agency as possible, so long that it does not harm anyone. All debates in Western society, from guns to taxes to drugs to gay rights, are just fine-tuning of this abstract of the free individual. We however do not subscribe to this paradigm. Even those thinkers who produced this paradigm (John Stewart Mill and others) didn't claim that it was the end-all be-all metaphysical truth of human existence. We believe that Allah created us to know Him (51:56), and the first step to knowing Him after we have established His Existence and the validity of His Messenger (s) is to submit to Him. Then, it is to trust Him, then it is to always be wary of Him, then it is to know Him. Part of understanding this reality is accepting the fact that there are sexes, and that sexes are not just a figment of our imagination - they really exist, and they are different.
6. There are rules, and there are exceptions. The rule in warfare is that men are more physically and emotionally capable for conscription. The exception is that boys and elderly men are not fit for warfare, and so they are not conscripted. Many similar rules and exceptions apply to issues of sex. One problem with the neomasculine movement is that not all men are Arnold Schwarzenegger, and in Islam not all men have to be. Similarly, not all women are soft and motherly, and Islam does not dictate that they need to be this way. Find what you are comfortable with, so long that it fits within Islamic ethics and justice. Technically, in the shari`a, a woman does not even need to cook, clean, or breastfeed her kids, all of that is her prerogative.
7. Although there are exceptions, be mindful of extreme ideologies. Human nature does not change overnight, no matter how progressive or "woke" a society is. Some of these ideologies have become a gateway drug to apostasy, and women (and now MGTOW men) are reaching for them because they can't find help or answers in our community.
There is much more to say on the subject, but this is a start.
We shouldn't be too obsessed with traditional masculinity or femininity, to a point where we assign gender roles.
Assigning gender roles is a bit absurd imo. Let people live and why should we force them to feel that aren't qualified to be Masculine or Feminine. I hear some ridiculous statements from "masculine" men that guys who cry are weak. Who are we to set these traits? These are definitely social constructs.
However I do admit that biologically we can draw the line between femininity and masculinity - in a general sense, not in a sense that "women should stay in the kitchen" etc.