Well, I think you've more or less explained my point exactly! The purpose of language is to convey meaning, and my using "their" for Google is precisely and intentionally in defiance of the idea that a corporation is inanimate. If you change that part of my writing, you actually change the entire voice and personality behind the writing!
And that's why it's so difficult to read the things that LLMs write. Because they follow the rules of language without embracing the chaotic nature of the fact that it's meant to convey information rather than to "be correct".
Another way to view this is as metonymy. "Google" is a metonym for "Google Staff", so using "their" to refer to the humans-making-up-the-corporation (as referenced by the metonym) is appropriate.
I agree it's correct English to say "Google have launched their new product".