I can understand the misconception that the API should work like the public chat app, but that is an app built on GPT, it’s an example.
What people fail to understand is that storing session data would incur a cost and require additional infrastructure. I could only imagine this functionality as a paid service. And while I could see openAI provide something like this, it does fall outside of its current domain.
If you are here to make an application, you need to understand you are building upon GPT, not ChatGPT. ChatGPT is the example application.
As a developer, you will be required to handle the API and navigate your interactions with the current restrictions in place. And though it definitely requires work and knowledge, I prefer the abstraction.
Good luck.