Here's redesign of ChatGPT focusing on Chat visibility.
Flow 1: User enters previous chat, Creates new chat , Enters another chat (Color change in type bar indicates a different chat). Views search and Filter options. 

here's Version - A of managing prompts in ChatGPT (From Type bar) (Press "R" to restart flow and "Z" to fit width)

Here's Version -B of managing Prompts in ChatGPT (From sidebar) (Press "R" to restart flow and "Z" to fit width)

Here's the wireframe and design components used in hi-fi designs.

Here's the case study of the Project, which includes UX research and ideation process.

Here's the Report of A/B testing conducted for finding better UX among both the versions of managing prompts.