I doubt any would be effective. Any companies that fired workers over the mandates did so because they made it a company policy that their workers must be vaccinated or perhaps wear a mask and undergo testing or be terminated. I'm not even sure the OSHA mandate ever went fully into legal effect. Companies can still have such policies too, so just because the mandate doesn't exist doesn't mean some companies won't continue to have vaccine and testing policies on the books. They're free to make their own corporate policies and so some may continue to have such policies even without the mandates requiring them to. Regardless of the arguments at hand, it has generally come down to an issue of employees not complying with company policy, which is legally a valid reason to fire an employee. So yeah, I'm not really sure any lawsuits could get very far. Besides, most of the court systems hugely side with corporations over any sort of worker's rights or protections when it comes down to it, even something like this.