If we do same work via Subscription and API , the subscription is way cheaper. So if we compare them yes they loose money.

Obviously, Anthropic is a private company, so nobody here is going to know their financials (who is at liberty to share them). I'm not GP, but I think it's reasonable to assume the subscription is priced based on average usage, and that's a major reason it's so much cheaper than API prices.

none of them are making any money yet. they all lose.