@awice Sorry, I don't know the space complexities of standard library sort functions, probably because I don't care :-P. I'm pretty certain they're O(n) or better and that's good enough for me.
Yes, Java's Arrays::sort is a Timsort "adaption" for objects and that quicksort variant for primitive types. Check out the sort method documentations on the Arrays doc page for some more details.
LeetCode sometimes/often (?) uses Lists instead of arrays, and List::sort is documented as using a Timsort adaption as well (unsurprisingly, as List automatically means objects, not primitives).