So I take that to mean Musk wanted a settlement as primary goal, and that the threat to OpenAI's reputation was just an (unsuccessful) means to get what he wanted. That isn't to say it wasn't personal for Musk, just that he would have preferred to have gotten paid.
As to Musk texting "By the end of this week, you and Sam will be the most hated men in America. If you insist, so it will be" when the settlement offer was turned down, while I'd agree there were a ton of super embarrassing details that came out I don't think Musk was successful in making them more hated than even he is. I don't even think this secondary goal was successful, even though there were a ton of juicy bits.
I think regardless it would be extremely hard for him to make people hate Altman et al. more than himself. Altman's flaws are more subtle and require paying attention to a pattern of behavior. Musk has beem pure cringe for 5+ years now.
Judging by the sheer number of journalistic investigations into OpenAI and the number of accounts of former employees, I would have expected that OpenAI being chaotic and poorly run is common knowledge by now and the lawsuit doesn't add much more to it.
Sometimes rich, powerful people do stuff that's irrational. When you see Trump attack Iran and you think "this doesn't appear to make sense," you can reason "there must have been secret intelligence proving that Iran was about to nuke Israel because otherwise it was a stupid move," or you can reason "it didn't make sense because it was a stupid move."
Really comes down to what you think his primary motivation is and what are just benefits.