Dr. Gay's credentials are, honestly, not that great. As an academic, her h-index is an unimpressive 11, but being a university president is largely not about being a well-respected academic (her predecessor had only 13). For comparison, a renowned academic like Kimberle Crenshaw has an h-index of 54.
(h-index is a measure of how heavily cited an academic is, which is a rough gauge of how important their scholarship has been, because people cite important work.)
However, being able to conduct oneself well in front of important parties is the core competency a university president needs. She screwed up really badly at key points in her Congressional testimony. She wasn't alone; all the university presidents made the same type of error, in the same way.
Fine, so own up to the mistake--Claudine Gay apologized--and keep going. Harvard's Board had her back. This is how academic freedom is supposed to work: mess up, but honestly, have the mistake demonstrated to you, you fix it and go on. But because a university president position isn't just an academic position, it's hard to argue it must be that way. It didn't save Larry Summers (h-index 138, by the way).
Anyway, whatever her good qualities are, having strong scholarly credentials isn't one of them. In that regard, she really doesn't stand out amongst her peers, even her black peers. Maybe when you talk to her in person, her degree of scholarship does seem exceptional, but if so, for whatever reason it's not reflected in her publication record, and that's most of what scholarly credentials are (for good or ill).