A session is not the same as a state.
The reason it is stateless is because you don't keep a constant connection to the server, but you send a request and get a response. Then the communication ends (simplified).
If you take a protocol like SSH or FTP, it can be in a state of connected, because it keeps up the connection. If something interfere with the connection (ie you lose WiFi) the state is broken, where in HTTP you can be disconnected and reconnected and the server will never know.
The session is a short term reference to your session, but it's not a state. Sure if you go into the details, the server (but this is not a part of the HTTP protocol) will have open and closed sessions which might be seen as states.