Wokeness is an extension of what is called 'identity politics': the idea that political action and emancipation is leveraged by and for specific identity-groups or cultural niches: ethnic, gender, religious, racial, national... it took the place of 'traditional' emancipatory political agendas centered around predominantly class status.
It became the predominant form of social democratic politics levered by the Western left roughly since the Civil Rights movement in the 60s, and continued through the gay and lesbian rights movement. It also coincided with the development of specific developments in the critical humanities and new theoretical paradigms in philosophy and the social sciences: critical theory, postcolonial studies, third-wave feminism (Butler, Wittig...), intersectionality studies (Crewnshaw), deconstruction (Derrida), Foucaultian genealogy, new orientations in Marxist criticism, indigeneity studies, liberation theology and dependency theory, historiography... just to name a few. The major idea was complicating the 'economicist' tendencies of orthodox Marxian theory and its offshoots to think of other forms of determination beyond class, their interactions, and to think of ways to go beyond the residual occidentalist, Eurocentric, Hegelian-metaphysical, teleological undercurrents in Marx...
There are several recurrent tropes that come from these vectors of thought, some of which are:
1) The deconstruction of conceptual binaries: This is an extension of the critique of metaphysics initiated by Heidegger and extended by Derrida, Foucault, and others through historicist, deconstructionist, and genealogy methods. What begins with an assault against foundational antinomies in Western philosophical history (eidos/soma, soul/body, res cogitans/res extensa...) becomes extended into a general critique of how specific conceptual oppositions have operated normatively to generate systems of exclusion and benefits, often through underwritten assumptions. Third wave feminism was central to this, and Butler's Gender Trouble remains, in my view, the essential book, in the extension of this to gender/sexual binaries. Others have attempted similar operations in other registers.
The whole 'gender pronoun' thing, for example, stems from youth culture groups in American schools influenced by these trends, trends which are present at the core of curriculae in the Humanities in the academy and the social sciences, and arts, e.g. American Latino immigrants and their generational descendants coined the Larinx movement as a way to think of the relation between language and power relations, extending on what Butler had already worked in her critique of gender/sex binarism.
2) The critique of Occidentalism and colonialism: Extending on the critique of imperialism leveraged by Marxist scholarship, a more attentive relation to how processes of colonization since the 16th Century have shaped not only the history of geopolitical violence and its concomitant phenomena (slavery, capitalism, neofeudal landlord oligarchic systems...) but also cultural expansionism and ideology. This has also allowed for a different conception of racism to be extrapolated from the traditional subjectivist definition, in what is termed "structural racism" today. The 'structure' part is a direct reference to how structuralist and poststructuralist theoretical approaches (notably coming from post-War French philosophy and social sciences) recoded certain tenets and methods of historical materialism through the extension of structuralist analysis, e.g. Althusser, Balibar, Ranciere; more recently, Zizek, Badiou, Ranciere...
3) A generalized social constionist approach to categories that are often taken as natural, or given: sex, gender, morality.... often times this leads to a difficult negotiation between a kind of cultural relativism (who are we to judge others) and the defense of minoritarian/vulnerable population rights (we ought to defend against the abuses to women/indigenous groups...)
Has it gone "too far"? Well, it is clear it has succeeded on many fronts and failed in others, and it has definitely generated a kind of violent reactionary trend that feels almost by sheer antagonism the compulsion to recoil into radical forms of essentialism, binarist, even facistoid and nationalist sentiments. This is the result of 'woke culture' taking a specifically ineffective approach to advancing their causes, most notably the whole "cancel culture" phenomenon which collided very strongly not only with 'libertarian' oriented people, but with the very youth-cultural impetus who doesn't like to be told what they can and cannot say.
Above all, the woke-left, I think has to be blamed for allowing issues of class inequality to slip in favor of identity politics, to the point of disenfranchising the white working class in many parts of the world. The so-called "Alt-Right' has done very well in seizing this gap through new forms of populist, xenophobic, and pseudo-technocratic ideology. I think the left is in dire need of restructuration, and that the dominance of woke culture in the academy and mediatic apparatus is holding the left back from this, having transformed these organs into essentially propaganda machines (what Moldbug and NRx people name The Cathedral).
But as with everything, it is important not to throw the baby with the bathwater.