Pedantry: (wrt all) an arbitrary counterexample would be Abramsky, Domain Theory in Logical Form (1991), which is a 20th century tract on logic, but (although they may share a common Limit between them) is also something Other than a response to Hegel.

Its difficult to tease these things out, but Hegel was the dominant philosophical force of the 19th century in the UK, so any logic immediately following that period had to deal with the immensity of his influence. True, once we get to the 90s, its not clear if the authors are entirely aware of the intellectual history and are just building off of ontologies that they have uncritically adopted as "logic," but in broad strokes it is still the case that the development of logic in the 20th century is as a direct response to Hegelian philosophy.

In other words, Nothing called so much of 20th century logic into Being as Hegelian Becoming?

There is no becoming in Hegel

I'd have to read more (or get clarification here) to understand what you mean; pp82-106* of a translation appear to cover a fair amount of Becoming to me?

https://archive.org/details/georg-wilhelm-friedrich-hegel-sc...

* including subheads such as "Moments of Becoming" and "Sublation of Becoming".

(ok, reading pp106-108 suggests that although Becoming is not Nothing for Hegel, it is self-contradictory and hence a special kind of a non-being, a determinate being?)

You should start with the Phenomenology of Spirit