Desktop app: switching accounts loses all conversations and sidebar state

Problem

When hitting usage limits on Claude Code Desktop App (Mac), there's no way to switch to another Pro/Max account and continue working without losing all conversations and sidebar state.

Current behavior: Logout → Login with different account → all conversations gone, sidebar reset. Must continue in CLI, then hand off back to desktop — double token spend on handoffs + significant time waste.

Codex comparison: Codex CLI allows logout/login with another account and continues without interruption.

Impact

• Double token spending: handoff from desktop → CLI → desktop requires summarizing context twice
• Time waste: 10-15 min per account switch for context reconstruction
• Especially painful for users with ADHD who rely on visual conversation history

Requested behavior

• Conversations should persist locally across account switches (they're local data, not account-bound)
• OR: allow multiple accounts and switch between them without clearing state
• At minimum: preserve the sidebar/conversation list so users can resume where they left off after re-login

Environment

• Claude Code Desktop App (Mac)
• macOS Darwin 25.3.0
• Multiple Pro/Max accounts