Looks like age <13 SATs are back, with a new parental consent form and a few extra logistical hoops. But also a possibly a digital option, which may address some of the questions regarding testing in a roomful of big teens. (I think it's probably still at a testing center, which might be with adults, which may or may not be an improvement for certain children.)

https://satsuite.collegeboard.org/sat/registration/additional-registration-options/students-under-13

...pronounced like the long vowel and first letter of the alphabet...