Altman won't be starting a competing company. First, he may have contractual restrictions and second, OpenAI owns their IP. And even if Altman is somehow free to do what he wants because he was fired (doubtful), anyone who quits to go with him surely do have airtight non-competes. Besides, it's not like Sam and his few loyalists are just going to spin up a few servers and duplicate what OpenAI has done. He'll do something AI-adjacent like the chip startup he was rumored to be pursuing.
As for Microsoft, they have a contract with OpenAI and are deeply reliant on them at the moment. OpenAI isn't disappearing just because Sam and Greg aren't there. Nadella may not be happy with the change, but he'll just have to live with it. Nothing will change for the foreseeable future there either.
When it comes to lawsuits? Who knows, but I highly doubt Altman will fight, or if he does, it will be discreetly settled as it's in no one's interest to wage some protracted battle. Microsoft may want to renegotiate their deal, but that again most likely isn't going to be anything nasty, as Microsoft needs OpenAI right now.
As for developers and consumers of OpenAI's service? They won't care or notice for many months until whatever changes the new CEO and board have in mind are enacted.
noncompetes are illegal in california