Specifically, neutrino oscillation is experimentally confirmed, but my understanding is that you can't just bolt it on to the Standard Model without getting inconsistencies unless you make one of the following two changes: Either make neutrinos their own antiparticles, or introduce sterile neutrinos. That seems like a pretty good reason to look for sterile neutrinos!
Also, I have to disagree with what she says about dark matter (or modified gravity, the distinction is irrelevant here -- both presumably introduce new particles); to say "All we need to know is the distribution of it so we can make predictions, who cares what it actually consists of?"... to my mind the point of fundamental physics should be to build a complete model of the laws of physics, and that sort of instrumentalism is just giving up.
(We can also generalize from this to other cases where problems from cosmology or other areas of physics would seem to require explanations from particle physics, e.g., baryogenesis, since the Standard Model doesn't seem to produce enough CP-violation to explain that. I don't think it makes sense to exclude such indirect evidence from other fields when we speak of tests of the standard model.)
None of this is to disagree that there's a lot of work on what Hossenfelder calls "pseudo-problems", which I agree seems to have produce a lot of failed predictions for little reason.