Social Media has not distorted our sense of "self" - quite the opposite. We have, perhaps for the first time, a clear sense that "self" has always been an illusory construct.
That said, I'm inspired to know that people are reading Fichte and engaging the topic!
Interesting. Historically, a few readers of Goethe, Ibsen and Kierkegaard always knew that. It was contained. Maybe what's changed today is we are all confronted daily by horrifying evidence of the fragility of self-construction, and how precious it is - but without an explanation or coping method. Solomon and the terror management theorists don't fill those shoes any more than narcissism, and so perhaps we're headed on a trajectory back towards faith. Maybe that's the ultimate function of "social media", to show us why social media is inadequate to counter angst.
Same with self: it's not something that physically exists, it's a mental construct that can be useful or not, which can be amended and replaced in its position, taken apart, etc.
On one hand, the self is a bit uncomfortable to research and take apart because it's right inside "you" and is a part of the inside, but on the other hand it's extra convenient to study because it's always available.
Check out David Tang's lecture on QFT: "there are no particles, only waves" https://www.youtube.com/watch?v=zNVQfWC_evg
Mathematics still works (at our scale); the consequence is precision.
Individuation of anything is a construct - including subjects and objects:
Even setting aside the absurdities of reducing math to elementary arithmetic, and of reducing arithmetic to counting particular concrete things - claiming to have undermined math with quantum field theory is like writing an essay that argues against the existence of language. "There are no particles, only waves" is not QFT. It's a reasonable position for which QFT arguably offers some measure of support, but that's not even remotely the same thing. QFT is layer upon layer upon layer upon layer of deeply technical mathematics, with a bit of blind symbol-pushing to round out the rough patches.
If I have it right, the claim would be to undermine (the ontological basis of) logic itself, as the flaw is found, not in math, but in the underlying assumption in material, individual things - hence the connection to field theory. It may be more accurate to say that the flaw is not in logic or math, but in ontology - our understanding of what kind of things exist. From there, logic optimistically assumes a 'flawed' ontology.
For what it is worth, Roger Boscovich speculated on similar metaphysical claims in his 19th C field theory work.
Logic doesn't assume any ontology. You're free to treat it as a purely formal string-manipulation game if you really want to.
Approaching math or physics as if it were part of the humanities - close readings of primary sources, "genealogical" work, literary exegesis - is worse than useless. If you can't do math, you don't understand it. And if you don't understand math, productive engagement with the philosophy of mathematics is impossible.