fix(settings): case sync tests follow lastPickedCase, a failed pick is not undone, rollback is covered

- sync-case-state browser and stale-refresh tests use lastPickedCase (the stale test now fails without its guard)
- saveLastUsedCase runs on the case-sync chain, and the follow is skipped while this device's own pick was not stored
- _caseStateSyncOn tolerates a harness without loadAppSettingsFromStorage
- lastPickedCase added to the config-backup volatile-key test and docs; rename rollback tests cover caseSettings and lastPickedCase
- wiki row moved to System

docs/wiki/Settings-Reference.md

@@ -230,7 +230,6 @@ on. Details: [Custom Model Endpoints](Custom-Model-Endpoints#a-model-that-runs-o
 | Bypass approvals and sandbox     | Starts new Codex sessions with `--dangerously-bypass-approvals-and-sandbox`. Read [Agent CLIs](Agent-CLIs) before enabling. |
 | Allow network access             | Starts new local Codex sessions (Run menu, Resume and the API; not scheduled jobs) with `sandbox_workspace_write.network_access=true`, so commands in Codex's workspace-write sandbox can use the network. The [Codeman Skill](Codeman-Skill) needs it to reach this server from a Codex session. It applies to every such session, and those commands can then call Codeman's API, which can start a session outside the sandbox with no approval prompt, even when a password is set: see [Security](Security#what-codeman-does-not-protect-against). It applies where Codex runs the folder in workspace-write (a project you trusted in Codex) and does not change Codex's sandbox mode: a folder Codex runs read-only keeps the network closed, and Codex asks for approval per command. Synced, off by default; forced off for users without the privileged-commands grant in multi-user mode. |
 | Animated status effects          | Cosmetic.                                                                                      |
-| Sync cases across devices        | Keeps each case's **Agent Teams** and **Opus 1M** options on the server (`caseSettings` in `settings.json`) and, when you return to a tab, switches it to the case you last chose on another device. Synced, off by default. Without it each browser keeps its own options for a case (the case list itself is always shared). The case names are stored in the shared settings file, so a non-admin in multi-user mode neither reads, writes nor follows them. Each save sends only that case and the server merges it, so devices saving different cases never overwrite each other; a case renamed in Codeman keeps its options, and deleting or unlinking it removes them. A save the server refuses leaves the choice on that device only until the next sync, which brings the server's copy back, and says so. Only a case picked in a case picker is followed, not one a quick-start or an agent's spawned worker used. If another device turns this off, this one stops following, and the server ignores case options sent while it is off. Turning it off leaves the stored options in `settings.json`, so turning it back on brings them back. A device that already has options for a case keeps them until a device changes that case's options while this is on. |
 | MCP server sync                  | Copies the MCP servers each installed, enabled CLI (Claude, Codex, Gemini, OpenCode, Antigravity) and GitHub Copilot CLI has into the others' own config files. Synced, off by default, admin only in multi-user mode. Turn it on and **Apply** or **Save** (Apply keeps Settings open), then **Preview** shows what would change and **Sync now** applies it. It only adds missing servers, keeps the previous file as `.codeman-bak`, and leaves a file that receives env values or headers readable by you only. A config dir moved by `CODEX_HOME`, `CLAUDE_CONFIG_DIR`, `XDG_CONFIG_HOME`, `GEMINI_CLI_HOME` or `COPILOT_HOME` in Codeman's own environment is followed. |
 
 ### Notifications
@@ -259,7 +258,7 @@ Rebinding for the shortcut registry. See [Keyboard Shortcuts](Keyboard-Shortcuts
 ### System
 
 `CLAUDE.md` template for new cases, default working directory, the image watcher, the prompt-cache keep-warm default (**Keep prompt caches warm**, off) and its cap (**Keep warm for at most**, 2 hours after a session's last prompt; see [Keeping Agents Running](Keeping-Agents-Running)), and
-Cloudflare tunnel controls including the tunnel URL. The **Diagnostics** group runs
+Cloudflare tunnel controls including the tunnel URL. **Sync cases across devices** (under Paths, off by default): Keeps each case's **Agent Teams** and **Opus 1M** options on the server (`caseSettings` in `settings.json`) and, when you return to a tab, switches it to the case you last chose on another device. Synced, off by default. Without it each browser keeps its own options for a case (the case list itself is always shared). The case names are stored in the shared settings file, so a non-admin in multi-user mode neither reads, writes nor follows them. Each save sends only that case and the server merges it, so devices saving different cases never overwrite each other; a case renamed in Codeman keeps its options, and deleting or unlinking it removes them. A save the server refuses leaves the choice on that device only until the next sync, which brings the server's copy back, and says so. Only a case picked in a case picker is followed, not one a quick-start or an agent's spawned worker used. If another device turns this off, this one stops following, and the server ignores case options sent while it is off. Turning it off leaves the stored options in `settings.json`, so turning it back on brings them back. A device that already has options for a case keeps them until a device changes that case's options while this is on. The **Diagnostics** group runs
 `codeman doctor` on the server and lists the agent CLIs, tmux, Node and the optional office
 tools with their versions and install hints (admin only in multi-user mode). In multi-user
 mode, the **Users** administration entry is injected here.