[FEATURE] Persistent session context across model/provider switches within the same session

Preflight Checklist

• [x] I have searched existing issues and this has not been reported yet
• [x] This is a single feature request
• [x] I am using the latest version of Claude Code

Summary

When a user switches models or API providers mid-session (by changing ANTHROPIC_MODEL or ANTHROPIC_BASE_URL mid-conversation), the conversation context and memory state are not preserved across the switch. The new model/provider starts with zero context.

Feature Request

Add a session continuity mechanism that persists context across model/provider switches within the same running CLI session. Specifically:

1. Memory file state should survive the switch — if .claude/learnings/ or MEMORY.md were loaded before the switch, they should remain accessible after
2. Conversation history should be transferable — the message history from before the switch should be available to the new model/provider
3. Optional opt-in via flag — --preserve-context-on-switch to enable this behavior; off by default for users who want fresh starts

Why This Matters

Users on multi-provider setups (cost optimization, model routing, A/B testing) cannot switch models mid-session without losing all context. This forces artificial workflow constraints:

• "Don't switch models until you're done with this task"
• "Write everything to memory before switching or lose it"

Prior Art

• Issue #46420 describes the context loss bug this feature would fix
• The session storage layer already persists state across sessions — this feature would extend that to model switches within a session

Suggested Labels

enhancement, area:core, area:providers