[familyop]

I was wondering the same thing and did a quick search.

Employers can ask you for proof of vaccination, here’s why
https://www.nbc15.com/2021/04/20/employers-can-ask-you-for-proof-of-vaccination-heres-why/

Can businesses require proof of vaccination? Experts say yes
https://www.cbsnews.com/news/can-businesses-require-vaccination-proof-experts-say-yes/

Your employer can ask whether you’ve received the coronavirus vaccine — and even require it
https://www.washingtonpost.com/lifestyle/2021/03/06/workplace-covid-vaccine-policies/

Employers can require proof of COVID-19 vaccination — with some exceptions, EEOC says
HR Drive (human resources)
https://www.hrdive.com/news/breaking-employers-can-require-proof-of-covid-19-vaccination-with-some-e/592322/

Employers and Health Information in the Workplace
https://www.hhs.gov/hipaa/for-individuals/employers-health-information-workplace/index.html

[TChad]

From your first link:

Then, on March 23, a bill that would prevent employers from requiring the COVID-19 vaccine or mandating proof of vaccination passed in the Assembly. It still has to pass the Senate before it can head to Governor Tony Evers’ desk.

So states can override.