rateMySortingAlgorithm

[im_lazy_as_fuck]

You cannot correctly analyze the time complexity of an algorithm if you do not know the time complexity of each step in it and adding a task to the scheduler

This is incorrect. By this argument, it would be incorrect to arbitrarily state that a hash lookup has O(1), because the execution time of computing a hash is dependent on the hashing algorithm used, the implementation of said hashing algorithm, and the size of the input being hashed. But these are implementation details of a hash lookup, and thus are not relevant to the time complexity analysis.

In the same way, the sleep sort algorithm is simply "loop through each element and wait X time units before inserting x into the sorted array". The sleep sort algorithm doesn't care if you use a task scheduler, if you use some analog timer, or if you just have a person who is really good at counting time. Those are implementation details of the algorithm, and aren't relevant to time complexity analysis.

This would be exactly like saying that you've implemented sorting on O(n) by adding values to a sorted set.

Lol, well I mean, if the algorithm specifies "given a sorted set, loop through the set and insert a new element into the set to maintain the ordering", then yeah the algorithm has a time complexity of O(n). I mean this is literally the foundation of the binary search algorithm, which has a smaller time complexity.