Desktop: option to show only this device's sessions in the Code sidebar (opt out of cross-device session list)

Summary

In the Claude Desktop app (Code tab), the session sidebar now lists sessions from every computer signed in to the same claude.ai account. On a Mac that only ever runs its own local sessions, the sidebar is intermingled with local sessions started on a second Mac. This is new behaviour; until recently each machine only showed its own sessions.

Please add a way to keep each machine's sessions on that machine, for example:

1. A "This device only" option in the sidebar filter controls (alongside the existing status / project / environment filters), remembered per machine; or
2. A setting (Settings → Claude Code, or a settings.json / managed-settings key) to opt out of listing other devices' sessions in the sidebar; or
3. A Group by device mode in the sidebar, so other machines' sessions collapse into their own section.

Why

• Two Macs used for different work end up with one long merged list, and it is easy to open a session whose working folder does not exist on the current machine.
• The existing filters do not help here: both machines' sessions are environment Local and can share the same project name, so neither the environment nor project filter separates them.
• Archiving is not a workaround, since archiving hides the session on the machine where it actually lives.

What I checked

• Desktop docs list only status, project, and environment sidebar filters: https://code.claude.com/docs/en/desktop#work-in-parallel-with-sessions
• No key in the settings reference controls cross-device session visibility: https://code.claude.com/docs/en/settings-reference
• The local sidebar pointer files under ~/Library/Application Support/Claude/claude-code-sessions/<account>/<org>/ only contain this machine's local_* sessions, so the other machine's entries come from the account-level list.

Related: #74662 (sidebar list is server-backed per account), #67517, #52052.

Environment

• Claude Desktop 1.46388.1 (macOS, Apple Silicon)
• Two Macs signed in to the same claude.ai account, each running only local Code sessions