If you read the docs you just posted, it clearly stated the user param is only for abuse monitoring by OpenAI staff.
Also, f you want to maintain state, you need to write code to store messages and resend them (feed them back) to the API. You can search this site for how to do this as this topic has been discussed many times here.
OpenAI APIs currently does not manage user sessions. This code must be done by the application developer.
HTH
