[FEATURE] Option to disable cross-device session sync / keep sessions local per device

What happened
Starting around July 15, 2026, all my Claude Code sessions began syncing at the account level — every chat now appears on every device where I'm logged in (Mac desktop app, web, CLI). My local CLI version (2.1.191, from June 24) had not updated when this began, so this appears to be a server-side rollout rather than a client update.

The problem
I don't want all sessions visible on all devices. Different machines are used for different work, and there is currently no way to keep a session local to one device. The only workaround is archiving sessions, which removes them from the active list everywhere but doesn't stop the syncing itself.

Request
Please add a setting to control this — any of:

• An account-level toggle to disable cross-device session sync entirely
• A per-device setting (e.g. in settings.json or the desktop app) to keep that device's sessions local
• A per-session "local only / don't sync" option

Environment: macOS (Darwin 25.5.0), CLI 2.1.191, desktop app auto-updated

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