No, it's not real money. In this case, convertable notes are loans backed by stock. That's why the debt is valued so highly. The notes are still for the same amount of stock, but the value of that stock is inflated beyond reason. Either way, Anthropic is not on the hook for the cash value of the stock, just the stock itself.
This debt is essentially noting that Anthropic does not own all of this stock on their books, but converting it into cash-value to do so. If someone were to buy the company, like via an IPO, it would be important for them to understand how much of the comapny's valuation is actually owned by the company vs other entities.