Desktop app: session history lost when switching accounts

Problem

When switching between Claude accounts in the Desktop app (e.g., after one account's quota is exhausted), all session history disappears. The new account has no access to previous sessions.

This happens in both Cowork mode AND Code mode (local </> mode). Even though Code mode runs locally on the machine, session history is still lost when switching accounts. This is unexpected — if Code mode executes everything locally, sessions should persist locally too, like CLI does.

The CLI version does not have this problem, because CLI stores session data locally in ~/.claude/, independent of account.

Steps to Reproduce

1. Use Claude Code Desktop app with Account A (either Cowork or Code </> mode)
2. Create several sessions with conversation history
3. Account A quota runs out
4. Switch to Account B
5. All previous sessions are gone — even in Code (local) mode

Expected Behavior

Session history should persist across account switches, especially in Code mode which runs locally. Sessions should be stored locally (like CLI does), not tied to a specific cloud account.

Current Behavior

Sessions are bound to the cloud account in ALL Desktop modes, including the local Code mode. Switching accounts = losing all session context.

Impact

Users who rotate between multiple accounts (common when quota is exhausted) lose all working context — conversation history, in-progress tasks, debugging sessions. This makes Desktop significantly less usable than CLI for multi-account workflows.

The fact that even Code mode (which is supposed to be local) loses sessions makes this feel like a bug rather than a design choice.

Suggested Solution

• Option A: Store session history locally (like CLI does) regardless of which account is active, at least for Code mode
• Option B: Allow importing/linking sessions across accounts
• Option C: At minimum, warn users before switching that sessions will not carry over

Environment

• Claude Code Desktop on macOS (Apple M4 Pro)
• Multiple Claude accounts with subscription
• Affects both Cowork and Code (</>) modes