fix: apply the review items for #680 at merge

Restore settings.json (caseOrder, lastUsedCase) when linked-cases.json cannot be written, with the rollback test extended
List Claude Code's per-project ~/.claude.json entry as not migrated in Core-Concepts.md and CLAUDE.md
Say in the 500 that the folder is now at the new path when moving it back fails
Describe the rename dialog's folder checkbox in Core-Concepts.md, carry stoppedSessions on errors, count 5 case SSE events

Co-Authored-By: Claude Opus 5.5 (1M context) <noreply@anthropic.com>

docs/api-reference.md

@@ -1135,7 +1135,7 @@ A local case whose folder is the top of a git repository can keep **worktrees**
 
 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.
+`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 `settings.json` and the folder are put back (when the folder cannot be moved back, the `500` says it is now at the new path). An error from the rename itself carries `stoppedSessions`: how many sessions it ended before it failed. 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