[Feature Request] Add session persistence and recovery with named tasks

Bug Description
Feature Request: Task Persistence & Session Recovery

Pain points with current Claude Code CLI:

1. After compact, conversation history becomes invisible - I can't see what we discussed, only the model "remembers" internally

1. No session recovery after terminal disconnect/reboot (unlike Codex which has --resume <session_id>)

1. No way to name/tag tasks for easy return ("Feature X", "Bug Y")

1. Context gets lost between windows when using Claude Code + VS Code + browser

Suggested improvements:

• claude --resume <id> to restore previous session
• claude --list-sessions to see past work
• claude --task "name" for named persistent tasks
• After compact: show summary of what was done, not empty chat
• Session IDs that survive terminal restart

Use case: Working on a feature from start to finish without losing progress. Cursor solves this with persistent chat + file context. Claude Code has better model quality but worse orchestration.

Environment Info

• Platform: darwin
• Terminal: Apple_Terminal
• Version: 2.0.56
• Feedback ID: 16312a92-85e1-4b6f-ae7a-019102c6dcfc

Errors

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Additional context:

The core issue is context retention during extended sessions.

Observation: Claude in Cursor maintains task context significantly better than Claude Code CLI. In Cursor, the AI tracks the full scope of work - objectives, decisions, progress, and next steps - even across long sessions.

In Claude Code CLI, the model tends to lose track of the broader task context more quickly. This results in:

• Repeated questions about things already discussed
• Loss of understanding of overall task goals
• Need to re-explain context frequently

This appears to be related to how context/memory is managed rather than model capability itself, since the same underlying model performs differently across these interfaces.

Suggestion: Investigate how context summarization and task state persistence can be improved to maintain coherent task understanding throughout longer development sessions.