It doesn't matter if they're affected. A judgement is going to be for a dollar amount. A court will rule that Musk must pay twitter X billion dollars. Twitter can then pursue Musk, taking basically anything he owns in terms of business.

They could contact the broker holding his shares and restrain them, order them sold, and collect the proceeds.

They could seize and sell at auction the real property of any of his businesses. SpaceX rockets? Office chairs? Servers? Anything.

All of this enforcement costs money. Twitter would account for the money spent seizing assets and charge those expenses to Musk as well.

Assets seized in this way (including stock) are often sold for much less than they're ideally worth. It's Musk's problem. Twitter would be empowered to seize seize seize until they've raised enough cash to cover the judgement plus expenses.