From what I've seen so far, Slow Joe's handlers (he doesn't do anything except mumble off the teleprompter and soil his diapers), is to have OSHA write a Proposed Rule, following sort of the same process as ATF has done for the frame and brace changes.
Usually, the administrative agency proposes a rule, then there's a 90 public comment period (as there was for ATF's gun grabbing schemes), and the agency has to review the comments and address questions and comments. Then a Final Rule is published, with an effective date of it applying.
As for what they are going to do here with regards to timing and if there will be a public comment period - I've not seen that. They may say that ITS A BIG EMERGENCY!!!, and try to not have a public comment period. Any deviations from what they do in comparison to the standard procedure makes the Rule more vulnerable to challenge in court just for the technical aspects of how it was put into place, not even touching on the aspect of if OSHA can mandate vaccines or testing - it's my understanding that the Proposed Rule has weekly Wuhan virus testing as an alternative to taking the shot.
For Slow Joe's handlers, the important thing is that THEY"VE DONE SOMETHING!!!, as his big block of semi-swing voters, the suburban white women with college degrees (AKA the Karens) were starting to feel that he wasn't doing anything. So this helps him shore up support from the afternoon wino crowd.
If courts strike it down, then he can blame them for it all, which works just as well. Remember, the most important thing for Karen's is "feeling". Results don't matter, as long as you care and feel. Thank god we didn't have this foolish group of voters around for WWII - we'd have lost, as we have every war since.