What is topological about topological (Dirac or Weyl) semimetals?

The following is my rough understanding of topological phases of matter (please let me know if it is incorrect.) Topologically ordered phases of matter are topological in the sense that they are determined by their topological excitations, and specifically by the braiding and fusion of these. The topological data that classify topologically ordered phases are encoded in higher fusion categories. (There are also invertible topological orders, which have no topological excitations but have a non-trivial gravitational response.) SPT phases are topological in the sense of having topologically-protected, gapless edge modes, but are only non-trivial if we don’t break a symmetry $G$. The topological data that classify SPT phases are encoded in generalized cohomology theories depending on the symmetry $G$.

Dirac and Weyl semimetals are also referred to as topological phases of matter and called topological semimetals. In what sense are topological semimetals topological? What are the topological data that characterize topological semimetal phases?

There are several other questions on topological semimetals and on the meaning of topological phases in general, but I think this question is not a duplicate because I am asking specifically what topological data are used to classify topological semimetals.