So far, I have stayed away from discussing the OSHA ETS. My argument has been simply that the principle underlying the idea of "keep your laws off my body" should cause people who hold that idea to be opposed to vaccine mandates.
As far as the OSHA ETS goes, you are correct that it is a jab or test paradigm and, for that reason, I don't think it presents the same constitutional problems as the EOs that mandate vaccination for federal employees and contractors, which truly do mandate vaccination, subject only to approved medical and religious exemptions. It does, however, have its own legal problems, constitutional and statutory, as identified in the 5th Circuit opinion staying it. Most notably, to my mind, is the major questions doctrine, which the SCOTUS recently invoked to strike down the eviction moratorium, concluding that Congress didn't delegate authority to the CDC to freeze evictions. There are also significant statutory questions, including whether the OSH Act, which is supposed to apply to workplace hazards like benzene fumes from sealant removers, etc., etc., etc., applies to (a) viruses at all and (b) hazards that exist everywhere, not just the workplace. Also, it's pretty clear that the Biden Administration is simply using the ETS to get more jabs in arms, regardless of actual workplace conditions, and regardless of whether the ETS is a square peg for the OSH Act's round hole.
Even if you don't have a problem with the ETS from a policy perspective, I think it is unlikely to survive judicial review.