[FEATURE] Auto-continue in new conversation when context limit is reached

Preflight Checklist

• [x] I have searched existing requests and this feature hasn't been requested yet
• [x] This is a single feature request (not multiple features)

Problem Statement

When working on long autonomous tasks, the context window fills up and Claude stops. I have to manually:

1. Ask Claude to save progress to files
2. Open a new conversation
3. Paste a handoff message to resume

This breaks the autonomous workflow. I can't leave Claude running unattended on complex tasks because it will hit the context limit and just stop.

Proposed Solution

When context is nearly full, Claude Code should automatically:

1. Save current task progress to a handoff file
2. Create a new conversation in the same window
3. Load the handoff file and continue working seamlessly

The user should be able to come back and find the task completed across multiple conversations, without manual intervention.
I'm using Claude Code Desktop (Windows). This feature would be especially useful for the desktop app where long sessions are common.

Alternative Solutions

Currently I work around this by having Claude save progress to a knowledge base file, then I manually open a new conversation and paste a handoff message to resume. It works but requires me to be present.

Priority

High - Significant impact on productivity

Feature Category

Interactive mode (TUI)

Use Case Example

1. I ask Claude to build a pet house system for my game (involves creating 10+ files, multiple systems)
2. After ~30 minutes of coding, context fills up
3. Claude has to stop and ask me to open a new conversation
4. I copy a handoff message, open new chat, paste it, wait for Claude to re-read all files
5. This happens 3-4 times per task, each time losing 5 minutes

With this feature: Claude would automatically continue in a new conversation and I could come back to find the task done.

Additional Context

_No response_