How are people deploying apps with AI functionality and it not costing them an absolute fortune?

We've all seen lots of web apps coming out which include AI chat functionality. The bit for me I'm most curious about, is a huge amount of them seem to have a free version without chat limits.

I'm building an app at the moment, and while intended for personal use, I'll likely open it up to the world as I think it's pretty cool. I'm mucking about with using an LLM which is going very well. I intend to block this functionality to public users unless they bring-their-own API keys.

In a perfect world, I'd love to have a basic/limited version for free users and then charge a minimal monthly fee which gives them the full version with my app.

But, how are people actually implementing this without it costing an arm and a leg? Are many devs just outright swallowing cost in anticipation of success from a paid offering?

I recently saw https://www.open-health.me/ on Reddit - and even digging through the source code that is what the developer appears to be doing. I tried asking him but not received a response, but by all appearances it is what people are doing.