Probably not since binary search is inherently sequential, and threading isn't useful in competitive programming anyway since online judges that I know of run on a single core and/or count the sum of the times taken by all threads.

why not? In normal binary search, we divide our interval into 2 subintervals, run 1 check function and achieve time complexity O(log_2(n)). With threading, we can divide it into 3 subintervals and run 2 check functions in parallel so time complexity is O(log_3(n)), etc.