Historically, in Classic Engine $group we use std::stable_sort: 

https://github.com/mongodb/mongo/blob/0a68308f0d39a928ed551f285ba72ca560c38576/src/mongo/db/pipeline/group_processor.cpp#L235

As stable_sort imposes additional restrictions, it performs slightly worse than just std::sort.

And in this case we know that all keys are unique (as they are keys from a map).

So it makes no sense to use stable sort.