> Do college educated people of color with tech skills currently have trouble finding work in the industry,

Compared to similarly-educated, similary-skilled white people, my impression is, on average, yes. (Where "people of color" is taken to mean "from groups underrepresented in technology"; there are certain non-white groups for which I don't get the impression that this is the case.) Largely because of network factors.

> or is the problem that there simply aren't enough people like that?

That's also a problem. The two are not mutually exclusive.