First-rate people attract other first-rate people, but second-rate people tend to hire third-raters, and third-rate people hire fifth-raters.
This is a quote from Paul Halmos, who attributed the idea to Andre Weil.
Outside of the top universities, relatively few US research universities have significant Theory groups in CS departments at all, because people doing theory research don't tend to bring in million dollar grants.
Outside of a few clusters, mostly at top universities, relatively few US research universities have logicians in mathematics departments, because the perception amongst most mathematicians is that logicians work in a completely disconnected area of no interest to mainstream mathematicians. (Logicians have not helped themselves in this regard.)
EDITED TO ADD: My impression is that categorical logic, homotopy type theory, and related areas have been somewhat exempted from the difficulties logic has as a subfield because a lot of the interest in it comes from people who were trained, and in many cases first earned tenure, as algebraic topologists or algebraic geometers. However, this doesn't help someone coming into the area whose background is in logic rather than algebra.
Outside of top universities, it is hard to get hired into a permanent position at a mathematics department in the US without some North American teaching experience. You can get this experience as a postdoc, but you'd have to first get a postdoc.
If it turns out that you really are first-rate, and first-rate in logic usually means being at least arguably the single best logician on the job market that year, then I think it doesn't matter much. Part of being a first-rate department and hiring first-rate people is understanding that the title on your degree doesn't mean much.
If it turns out that you're not first-rate, then the job market for logicians in the US has been terrible for many years - it's easily been the worst among the major subfields of mathematics - and the economic crisis associated with the pandemic can only have made it worse. In the general mathematics job market, doing a PhD in Europe and not having US teaching experience as part of your PhD puts you at a disadvantage, and not having mathematics teaching experience (as part of your PhD or afterwards) also puts you at a disadvantage. (CS works somewhat differently because administrators love those million dollar grants.)
