I live in California, I read national media for decades, and I've never heard of it.
When I google for it, the top-10 news hits for it are mostly NYPost, City Journal, NBC New York, NYDailyNews, also Manhattan Institute, TheNation.
Even if you google "SHSAT site:latimes.com" you only get hits for NYT, etc.
SFChronicle has only ever mentioned it once, and that was in 2021 in the context of the local (SF) debate about Lowell HS's entrance exam: (https://www.sfchronicle.com/bayarea/article/S-F-s-Lowell-isn...). Googling "site:sfchronicle.com SHSAT" only has that one hit.
