[Feature Request] Persist conversation state to recover from unexpected terminal closure and compaction

Question

**Bug Description**

I don't like the way CC loses the most recent conversation during compaction or even when my Terminal unexpectedly closes. It would be great to have continuity after unexpected errors.

**Environment Info**
- Platform: darwin
- Terminal: vscode
- Version: 2.0.25
- Feedback ID: cc6e1ec3-2eb5-449f-9a78-33042435dcd1

**Errors**
```json
[]
```