Absolutely. I don't know what legal jurisdiction they are subject to, but I could imagine that someone tries to sue an EU division/outpost in an EU court under a GPDR-type of petition, these posts would be submitted as evidence. One could easily argue the CEO is acting on behalf of the company by posting using their real name. (Let's presume there is no identity fraud for these posts.)

And don't forget that Elon Musk was tried in the US for defamation after making a bunch of posts on Twitter against some UK citizens. Assuming that you are posting under your real name, you are definitely legally responsible for those words.

Anything a publicly traded company would state that would lead to a person making a decision to buy or sell stock would be subject to FTC regulations.

And if it is not a publicly traded company? Can the CEO in question making statements and assurances on a forum or linkedin or X in communication with a user cause the company to be in a binding position?

Or would it be an empty promise?