Thanks for the link, that looks cool! Unfortunately, I don’t know of a julia package for optimal transport.
From a (very) short glance at the source, it looks like POT is doing most of the numerical heavy lifting in C/C++ libraries, but the python code is also non-trivial.
If this is correct, then PyCall looks like a good choice (no big speed-up if POT is already using fast C code; calling the C-libs from julia would be non-trivial because the python code is not just a thin wrapper but contains real logic). Of course, if you want to experiment with new algorithms for optimal transport, then this state of affairs sucks (two language problem); also it costs you heavy dependencies.
Is this assessment correct? You probably know more about POT than me.
I never used POT, but they do offer a buffet of solvers, spent the effort to offload a lot of computation into faster languages, and the choices like sinkhorn vs direct solver are probably more relevant than choice of programming language anyway (algorithm class very often beats implementation / hardware). Not sure how fast they are compared to other existing libraries.
Or are you in the situation where you want to solve many cheap OT problems instead of few expensive ones? Then you are in a bad situation, I fear 