Immunization status has never really been considered private. It’s been the norm for 100 years for immunizations to be disclosed to schools, to foreign governments for international travel, to certain types of employers, etc.
And it’s important to note, companies are requiring vaccination status whether you’re hybrid or fully remote. Fully remote offering no exposure risk to the company.
Some companies are already charging un-vaxxed employees higher health insurance premiums just for this reason.