Right, but most browsers aren't owned by money-losing startups desperate for any bit of training data they can get their hands on as scaling taps out.
I really doubt OpenAI consciously wants my passwords, but I could absolutely see a poorly-coded (or vibe-coded, lol) OpenAI process somehow getting my keychain into their training set anyway, and then somebody being able to ask Chat-GPT 6, "hey, what's Analemma_'s gmail password?" and it happily supplying it. The dismal state of LLM scraper behavior and its support (or lack thereof) of adherence to best practices lends credibility to this.
You miss the most questionable bit which is asking for keychain access. I said no to that one.