I don't think Anthropic and OpenAI will IPO at all. Word is that Anthropic will have $100 BN in revenues this year, and very likely OpenAI will get some similar amount. You IPO when you need money, and I think Anthropic and OpenAI are past that point.
You also IPO if your investors want to cash out.
They want to spend over $200B/year on $100B of revenue so they still need investment.