FWIW, I think the OSHA/ETS cases are decided and just die at the original jurisdiction, Circuit Court level.
ETS have a statutorily limited life of six months. ETS must be followed by a permanent rule. Those are litigated following the usual path starting at District Court.
https://crsreports.congress.gov/product/pdf/R/R46288 <- has summary of ETS cases
This vaccine has been out for almost a year. Absolutely no reason that the federal government couldn't have tried to move a mandate through OSHA via normal rulemaking or even Congress 6+ months ago rather than issuing this last second "emergency" action.
On that basis alone this rule deserve to be laughed out of court. That's not to say that the rule isn't invalid for a bunch of other reasons as well, but that one fails right out the gate.