The OSHA mandate is more likely to be upheld than not and even if it does get struck down, Roberts is likely to vote in favor of upholding it.
You're probably right. I do think Roberts will uphold it, and it will probably be upheld by the Court in general, by something like 6-3 or 7-2. The three liberal justices, along with Roberts, Kavanaugh, Barrett, and possibly Gorsuch, would comprise the majority. Alito and Thomas are the two justices who I see voting against it at this time.
Hmmm... I see Gorsuch as the surest no vote, and Thomas as a nearly sure no as well. Alito is more comfortable with coercive measures in general, but I'm almost sure he votes with the "right wing" position in a case this politically charged.
But Barrett and Kavanaugh have so far been uninterested in any challenges to vaccination requirements and the one time they struck a COVID restriction down, it was a really strict one (no in-person church for months in certain counties in CA) and they did it very narrowly. I would be surprised if the administration doesn't get at least one of them to uphold it, and the most likely outcome is they get both.