My prediction is that the court will deny the stay now but then eventually, years from now, undo the order by upholding a ruling against it once someone who has been harmed by it has standing.
The emergency rule by OSH has a 6 month life.
After that, the “regular” regulation will come into play, and be litigated starting from District Courts.
Unless SCOTUS rules that OOSHA has the power, in which case litigation is pointless, issue already decided.
Sotomayor says Omicron is as deadly as Delta. OMG, give OHSA more power. And what fed agency is in charge of masking in public?
There is immense immediate harm !