Anthropic was hiring a PM for Claude Tag last month. The pay was $385K to $460K. The listing said: "An engineering background is not required." That listing wasn't an outlier. Two weeks ago I had an AI read every open product job at 36 AI and tech companies: OpenAI, Anthropic, xAI, Databricks, Perplexity, Cursor, Figma, Stripe and more. 8,354 open roles. 781 had "product" or "PM" in the title. After it threw out product marketing, product design and sales roles, 651 unique roles were…