I don’t think the executive order has anything to do with International travel. The Federal government would set all requirements for International travel. If at the federal level they require proof of vaccination to get on an international flight there isn’t anything a governor can do about that.
I was referring to the state of FL being willing to link their state vaccination data to a potential federal vaccine passport system. If FL government agencies are not allowed to share people’s vaccination status then that could be problematic for people living in FL if they want to participate. Any federal system would rely on accessing state databases since to my knowledge we don’t have a federal database of everyone who has been vaccinated. That system would also likely be run by a third party similar to the trial system setup in New York.
From the Executive Order:
Section 1. No Florida government entity, or its subdivisions, agents, or assigns, shall be permitted to issue vaccine passports, vaccine passes, or other standardized documentation for the purpose of certifying an individual's COVID-19 vaccination status to a third party, or otherwise publish or share any individual's COVID-19 vaccination record or similar health information.