Your question is both simple and complicated because it will depend if the business is impacted by an applicable EO.
For example, a defense contractor could be impacted by an EO, but a food processor may not. There are legal limitations on EOs, and they commonly pertain to the executive branch operations and management under existing laws passed by the Congress.
Some businesses might be reading the tea leaves, or are led by big demonkkkrap donors, etc, so they may take it upon themselves to “get ahead” or support the aims of Xiden even though there is no legal obligation to do so. I just read some businesses in my area that cater to the public now want proof of vax or CCP-virus free (test = negative) else they will not serve you. There is no EO involved, nor local ordinances. But they are all demonkkkrap run businesses.
I would think that those businesses run by Dems that are asking for proof of shots or negative tests would be inviting lawsuits, on the basis that there’s no law allowing them to demand those things.
Speaking of EO’s I saw on FR the two hidenbiden EO numbers (one for fed workers & contractors, other for the private businesses 100 employees), but can’t find it now.
Do you know what those numbers were?