I am not a physicists nor a mathematician, so I am really just a layman
when it comes to the mathematical calculations of network science. Sorry if
my question doesn't make sense. However, I've read in a few papers*
suggesting that the calculation of centrality measures for multilayer
networks are a bit different than for single layer networks. I would like
to know if graph-tool incorporates this advances in the literature, does it?

If you look closely, you will notice that in most cases the definition of
most centrality measures for multilayer networks is identical to the
classical "monolayer" case, with the only difference that we need to
differentiate between copies of the same node in different layers, and the
connections between layers. So all you need to do is use the exact same
algorithms for monolayer networks, but represent the multilayer graph as an
edge-annotated monolayer network, where each node appears multiple times for
each layer it belongs, and their copies are connected by intra-layer edges.