I am not sure that it influenced async in javascript. But the earliest monad paper I found in ~2 minutes of googling [0] even uses natural transformations which in my opinion counts as using CT.
Async/await comes originally from F#, brainchild of the Cambridge MSR lab that also maintain(s|ed) GHC. Async/await is just a limited monad syntax, and its originators were well aware of that fact. Insofar as monads are a categorical vocabulary for effects, then, async/await in JavaScript and all the other languages that now implement it all ultimately stem from category theory :)
More vaguely but also more sweepingly I think the general approach, now the standard in language design, of taking a pure language as base and then adding effects to it is established thanks to Moggi's work on monadic effects, which makes essentially all modern programming languages heavily influenced by CT (at a couple of steps' removal).
[0] Eugenio Moggi Computational lambda-calculus and monads (1989) https://www.cs.cmu.edu/~crary/819-f09/Moggi89.pdf