I live in upstate New York - one of the more aggressive states for COVID measures - and have not yet had to do this, a year and a half into the pandemic.
(I did, however, have to prove my vaccination status and present ID when I became a naturalized US citizen quite a few years ago. https://www.uscis.gov/policy-manual/volume-8-part-b-chapter-...)
> And for schools, didn't you used to have private schools or homeschooling as an option to avoid these kind of mandates?
These still exist.