From – https://newmaterialism.eu/almanac/p/performativity.html

• re Derrida and Austin’s Theory of Speech Acts, Judith Bulter develops the idea of sexuality and gender as performative
• “Butler has put it herself: “This very concept of sex-as-matter, sex-as-instrument-of-cultural-signification […] is a discursive formation […]” (ibid., p. 50).”
• “Haraway’s notion of the material-semiotic that thinks the material, bodily fleshiness and the discursive-linguistic together, and thus breaks through the long-standing nature/culture divide (see e.g. Haraway, 1988 and 1997) – critical re-readings and re-engagements with Butler’s notion of (gender) performativity slowly but surely came into being”
• “For Barad, performativity is not only linked to the coming into being of the human subject and the (gendered) materialization of bodies, and the socio-political interpellation process that goes along with it (i.e. Butler’s more recent understanding of performativity as articulated in Bodies), but is about the processes of the materialization of “all bodies” and the “material-discursive practices” that engender differences between for example human and non-human bodies (Barad 2003, 810).”
• Matter is not a passive actor – (i.e. body/camera, body/phone – see Charlotte Prodger, phone shot on phone)
• Barad “moves away from an individualistic atomistic metaphysics, the modern Cartesian mind/body split, our strong cultural belief in representationalism, our Western tendency to thingify or basically objectify, and a mere discursive-linguistic concept of performativity”
• “but bodies themselves “come to matter through the world’s iterative intra-activity – its performativity” (ibid., p. 824).” So  – intra-activity is performativity in Barad’s theory. Rovelli talks about reality being relational  – “reality is reduced to relation” “We, like waves, and like all objects, are a flux of events; we are processes, for a brief time monotonous…” Events, therefore, are performances, using Barad’s language.  (Rovelli, 115/116)
• “Reality, according to Barad, is rather “a dynamic process of intra-activity” or “an ongoing open process of mattering through which ‘mattering’ itself acquires meaning and form in the realization of different agential possibilities” (ibid., p. 817).” So – therefore exactly what I have been unraveling and which is explained in the Hoffman book, Systems Theory, Rovelli etc. Barad applies it to the humanities and is interdisciplinary or in her words discursive and diffractive (I think?).
• “Materiality is no longer “either given or a mere effect of human agency,” but rather “an active factor in processes of materialization” (ibid., p. 827)” See the previous point.

Susan Yi Sencindiver on the Oxford Bibliography website writes: “Important as this [constructivist] ideological vigilance has been for unearthing and denaturalizing power relations, and whose abiding urgency new materialism does not forego, the emphasis on discourse has compromised inquiry by circumscribing it to the self-contained sphere of sociocultural mediation, whereby an anthropocentric purview and nature-culture dualism, which constructivists sought to deconstruct, is inadvertently reinscribed.” (2017)  https://www.oxfordbibliographies.com/view/document/obo-9780190221911/obo-9780190221911-0016.xml