You are reading the pre-existing statute. The green text are the additions that were passed, and the red text is what was removed.
https://www.flsenate.gov/Session/Bill/2021/2006/BillText/er/HTML
What passed was entirely positive:
An educational institution as defined in s. 768.38 may
not require students or residents to provide any documentation
certifying COVID-19 vaccination or post-infection recovery for
attendance or enrollment
A business entity, as defined in s. 768.38 to include
any business operating in this state, may not require patrons or
customers to provide any documentation certifying COVID-19
vaccination or post-infection recovery to gain access to, entry
upon, or service from the business operations in this state.
The offending section I cited wasn’t removed.