Plausibly part of the chain of events, unlikely to be a cause in itself. Nothing pops because of an underperforming IPO.
Though Anthropic's IPO flopping might affect the valuation of OpenAI, which further inhibits their ability to raise additional funds (which they're already been struggling with). Given the incestuous financing in AI any major actor in the AI space defaulting could bring a lot of companies with it.
As a side note, regardless of outcome, Anthropic IPO:ing is the first step in the inexorable march toward profit maximization and enshittification. You all better be ready with your verification cans.
With Anthropic's IPO (and I was looking forward for OpenAI as well) there should be some hope for some rationality to come back into the sector.
If the bubble bursts, better now than much later. The industry stance that's been ongoing "AI, at all costs" has been such a market and economic pressure on the everyday worker that even a small value deflation I deem necessary.