Add cloud sync with Browser Use browsers using bring-your-own API key

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Problem

Users should be able to sync with Browser Use browsers from the desktop app. This likely requires a bring-your-own Browser Use API key flow so users can connect their own Browser Use account or cloud environment.

Scope

• Add a settings/onboarding path for users to provide and manage a Browser Use API key.
• Store the API key securely using the existing credential storage approach.
• Define what syncs between the desktop app and Browser Use browsers, such as browser/session state, profiles, or other supported artifacts.
• Handle auth failures, revoked keys, missing subscriptions, and network errors with clear user-facing states.
• Avoid syncing sensitive local data unless the user explicitly opts in.

Acceptance criteria

• Users can add, validate, update, and remove a Browser Use API key.
• Cloud sync can be enabled/disabled from the app.
• Sync status and errors are visible and actionable.
• API keys are never logged, printed, or stored in plaintext app files.
• The implementation has tests for credential handling, sync enablement state, and API error handling with mocked network calls.