The big "make everything stateless" hype is just that: hype. Your server-side application code, should usually be stateless, because this makes your application more resilient to errors, easier to scale, and easier to reason about. But there are exceptions to even that, especially for stuff like video game servers.
Your services are almost always going to be stateful, and should be. If you have a database, files, or literally anything that affects the responses the server sends, then the service is not stateless.
So building "stateless" services is a lie. You shouldn't strive to make your services stateless, you should make sure you're putting your state in the correct place.