I'd like to know about the structure of chatGPT operation. About server and client

I am writing because I have a question about the chatGPT operation structure.

I think the question may be ambiguous.
Please reply if anyone knows, thank you.

I wonder if the session that sends the prompt in web chatGPT and receives the completion is saved in the OpenAI server or in the user account.

And in a previous question, it was answered that web chatGPT uses a truncation algorithm that summarizes conversations by analyzing key words, rather than generating answers by remembering all conversations. I wonder if this algorithm is running on the client (user account) or the server.
When sending a new prompt, I wonder if it is a method of applying an algorithm to transmit past conversation data, or if the OpenAI server stores past conversation data and applies the algorithm when a new prompt is sent.

Personally, I think that when sending a prompt, the prompt content and key value will be sent together and sent to the OpenAI repository.

The reason for asking the question is that additional development is required when trying to pre-enter information beyond a fixed token like chatGPT. At this time, I want to design what kind of structure to do.