Have you tried the Command Panel > Chat : Export Session ?

It allows you to export the Chat session that you have opened as json file.

expanding on this idea, 2 valuable use cases

• as an author, coming back to a proj x months later and having how-did-i-figure-this-out documentation. Having to import/export manually on every commit or session is cumbersome and prone to forgetting, and copypasta is prone to errors

• as a collaborator reviewing PR's, being able to see what assumptions guided the solution, having discussions on challenges, alternative paths not taken, etc

so, it would be nice that any assistant use automatically remembers. Brainstorming, maybe like

.chat
├── 2023-10-01/
│   ├── 94ignaf__how-do-i-set-up-vite.md
│   ├── 1a2b3c__fixing-webpack-issues.md
│   └── 7g8h9i__optimizing-react-app.md
├── 2023-10-02/
│   ├── 8k9l0m__using-async-await.md
│   ├── 2d3e4f__migrating-to-typescript.md
│   └── 5t6u7v__implementing-redux.md
├── 2023-10-03/
│   ├── 9o0p1q__debugging-node-app.md
│   ├── 3r4s5t__unit-testing-with-jest.md
│   └── 6v7w8x__working-with-graphql.md
└── 2023-10-04/
    ├── 0y1z2a__integrating-d3.md
    ├── 4b5c6d__building-rest-api.md
    └── 8e9f0g__managing-state-with-mobx.md

uid's guarantee uniq, but also human readable titles. This makes it easy to scan by topic, whether in a code editor or a cloud repo UI.

Ideally a standard emerges, so as chat becomes ubiquitous, diff layers of the dev process stack respect/expect/can use this metadata if the dir exists, in the same way a .git folder is universally understood:

• editors (VS Code with OpenAI GPT API or JetBrains on say Google Bard/Gemini)
• editor extensions (Continue wrapping Ollama locally on open models, Code Llama )
• agent/assistant apps (OpenInterpreter) and soon to come on the OS-level

You can now export a session as @tgrall pointed out, and you can also click the history button to use the persisted chat history that way.