feat(cases): rename a case and its folder, with a lock and live-session handling

docs/api-reference.md

@@ -1129,11 +1129,14 @@ A local case whose folder is the top of a git repository can keep **worktrees**
 | `PUT`  | `/api/settings`               | partial settings (strict schema)     | Merged into the stored file; services (watchers, tunnel, tmux history limit) reconcile to the merged result. `403 FORBIDDEN` for a non-admin in multi-user mode. A tunnel enable without `CODEMAN_PASSWORD` is refused separately (`403 OPERATION_FAILED`, resend with `acknowledgeUnauthTunnel: true`). |
 | `GET`  | `/api/execution/model-config` | none                                 | `modelConfig` (cron's and the plan orchestrator's default model). |
 | `PUT`  | `/api/execution/model-config` | `{ defaultModel?, agentTypeOverrides?, ... }` | Replaces `modelConfig`. `403 FORBIDDEN` for a non-admin in multi-user mode. |
+| `POST` | `/api/cases/:name/rename`     | `{ newName, renameFolder?, stopSessions? }` (strict) | Rename a case and its folder (see below). |
 | `PUT`  | `/api/cases/order`            | `{ order: string[] }`                | The one case order every user's `GET /api/cases` is sorted by. `403 FORBIDDEN` for a non-admin in multi-user mode. |
 | `PUT`  | `/api/config`                 | `{ pollIntervalMs?, defaultTimeoutMs?, maxConcurrentSessions?, respawn? }` (strict) | The process-wide app config in `state.json`. `403 FORBIDDEN` for a non-admin in multi-user mode. |
 
 A non-admin's `POST /api/quick-start` and `POST /api/ralph-loop/start` work as before but do not record their case as `lastUsedCase` (a server-wide key).
 
+`POST /api/cases/:name/rename` renames a case. A case under the cases directory is its folder, so it always moves; a linked case renames its alias in `linked-cases.json` and moves its real folder (next to the old one, named `newName`) only with `renameFolder: true`. Remote and Docker cases are `400`. The new name must be free in every namespace the list merges (`409`). Live sessions whose working directory is at or inside the folder that would move make it `409` with `requiresStop: true` and `sessions: [{ id, name }]`; retry with `stopSessions: true` to end them first (nothing is restarted); another user's session is `403`. The folder is held by an in-process lock for the whole operation (an overlapping rename is `409 BUSY`, and `new Session` refuses a working directory inside it), the move is retried for a transient `EBUSY`/`EPERM`/`EACCES` and then answers `423` with `renameCode: "LOCKED"`, a cross-device move is `400`, and if the registries cannot be written afterwards the folder is moved back. On success the response is `{ oldName, newName, oldPath, newPath, folderMoved, stoppedSessions }`; `caseOrder`, `lastUsedCase`, `linked-cases.json` and Claude Code's `projects/<path>` history are updated, and `case:renamed` is broadcast. A linked case is admin only in multi-user mode.
+
 ### System operations
 
 The same multi-user rule covers the operations that act on the whole server. For a non-admin: