feat(sidebar): manage folders that live under several model roots

The sidebar's folder tree merges every model root into one relative-path
namespace, but folder operations turned a node into a path by prefixing
default_*_root. A folder living under another root failed to delete with
"Folder no longer exists" (recipes under the primary lora root while
default_lora_root is the extra one), and where the same relative folder
exists in both roots the operation silently hit the other copy — 14 of the
16 top-level folders in the reporting library are shared, so guessing a root
was never safe.

Backend:
* ModelMoveService.resolve_folder() and GET /api/lm/{prefix}/resolve-folder
  answer which directories a library-relative folder maps to
  (folder_path/root/is_symlink), in scanner root order, skipping directories
  no root holds and refusing absolute or climbing paths.
* delete_folder/rename_folder tag a vanished directory with code "missing"
  so the sidebar can tell "this node is stale, refresh" from a failed
  operation.

Frontend:
* _resolveFolderCandidates() is the single place that turns a node into
  absolute paths: default root first, the old root-prefix fallback only
  while a single root is configured, and an explicit unresolved error for a
  multi-root library — nothing is guessed silently any more.
* One copy keeps the single-target modal, which now names the resolved
  absolute path. Several copies render one checkbox row per copy, each
  dry-run against the delete guard ("no models" / "contains N model
  file(s)..." / a deletion is still pending / no longer exists / symbolic
  link): a blocked copy is unticked, disabled and explained, the button
  reads "Delete N folders", every ticked copy is deleted and guarded on its
  own, and a partial failure is reported without discarding the successes.
* Rows are built once per open and only their status text is updated, so
  ticking a box no longer rebuilds the list, steals focus or resizes the
  modal mid-click; the action row keeps a fixed button width.
* Rename offers a root picker in its inline row, create inherits the
  parent's root when the parent resolves to exactly one directory, and the
  undo restores every copy a delete removed.

i18n: 26 new keys (sidebar.deleteFolderModal.*, .deleteFolderResult.*,
.renameFolderResult.*, .folderRoot.*, .folderResult.*) translated in all 9
locales, with the en wording normalized to the established "model root" noun
(it had said "library root") and the new terminology recorded in
docs/i18n-translation-guidelines.md.

Verified: pytest 3686 passed, vitest 1473 passed (86 in the folder-management
suite), pytest tests/i18n 20 passed, sync_translation_keys.py --dry-run
clean. A sandboxed standalone instance with two roots confirmed that deleting
one copy leaves the node in place, that the twin's model card survives the
purge, and that deleting both copies and undoing restores both directories.

docs/i18n-translation-guidelines.md

@@ -159,6 +159,27 @@ Locales: `en`, `zh-CN`, `zh-TW`, `ja`, `ko`, `fr`, `de`, `es`, `ru`, `he` (RTL).
 > holds again. The same pass scoped the client-side ETA to the current stage in
 > `static/js/api/baseModelApi.js`; no other locale string changed.
 
+> **Status (2026-10, multi-root folder resolution):** the folder sidebar used to turn a tree
+> node into a path by prefixing the *default* model root, so a folder living under another root
+> failed to delete ("Folder no longer exists") and a same-named folder in another root could be
+> the one that got hit. Folder operations now resolve a node through the backend
+> (`GET /api/lm/{prefix}/resolve-folder`) and act on the directories that really exist. When
+> several roots hold the folder, the delete modal lists **one checkbox row per copy** — each row
+> carries its own guard verdict, every deletable copy is ticked by default, and a copy that
+> still holds models (or is a symbolic link) is unticked, disabled and explained instead of
+> silently dropped. Deleting a subset leaves the node in the sidebar, because the folder list is
+> a union over the model roots; `deleteFolderModal.keptNote` warns about that before the click.
+> The scanner bookkeeping is root-aware for the same reason: deleting one copy no longer hides
+> the node until the next scan, and no longer purges the model cards of its same-named twin in
+> another root (rename keeps the twin's records untouched too). That added 26 keys —
+> `sidebar.deleteFolderModal.{missingTitle,missingMessage,symlinkTitle,symlinkMessage,confirmMulti,deleting,keptNote}`,
+> `sidebar.deleteFolderResult.{missing,symlink,successMulti,partial}`,
+> `sidebar.renameFolderResult.{missing,symlink}`, the 12 `sidebar.folderRoot.*`
+> chooser/status strings and `sidebar.folderResult.unresolved` — all translated in all 9
+> locales (terminology below). The `en.json` wording was normalized to the established **model
+> root** noun while translating (`library root` → `model root`, R5); the count-bearing
+> `successMulti` uses the singular `success` key when only one copy was removed.
+
 ---
 
 ## 1. Hard rules (do not violate)
@@ -499,6 +520,30 @@ placeholders. The keys carrying `{count}` are `successWithFiles`, `notEmptyMessa
 `notEmptyMessageExcluded` and `notEmptyWithCount`; `notEmptyMessageExcluded` is the only key
 carrying `{excluded}`.
 
+#### Multi-root folder operations (resolution, copies, symlinks)
+
+The sidebar's folder tree is a union over the model roots, so a relative folder can stand for
+several directories at once. Copy is called **copy** (one directory per root), never "version"
+or "instance"; a directory the backend refuses to touch is called out as a **symbolic link**,
+and a per-row verdict reads **no models** when the copy is deletable:
+
+| Term | Rendering |
+|---|---|
+| copy (one directory per root holding the same relative folder) | zh-CN 副本 · zh-TW 副本 · ja コピー · ko 복사본 · fr copie · de Kopie · es copia · ru копия · he עותק |
+| symbolic link | zh-CN 符号链接 · zh-TW 符號連結 · ja シンボリックリンク · ko 심볼릭 링크 · fr lien symbolique · de symbolischer Link · es enlace simbólico · ru символическая ссылка · he קישור סמלי |
+| unchecked (row / note wording) | zh-CN 未勾选 · zh-TW 未勾選 · ja チェックを外した · ko 선택하지 않은 · fr non cochée · de nicht angehakt · es no marcada · ru неотмеченная · he שלא סומן |
+| "no models" (row verdict) | zh-CN 无模型 · zh-TW 無模型 · ja モデルなし · ko 모델 없음 · fr aucun modèle · de keine Modelle · es sin modelos · ru моделей нет · he אין מודלים |
+| model root — plural ("more than one model root", "from {count} model roots") | zh-CN 模型根目录（多个模型根目录）· zh-TW 模型根目錄（多個模型根目錄）· ja モデルルート（複数のモデルルート）· ko 모델 루트（여러 모델 루트）· fr racine de modèle (plusieurs racines de modèle) · de Modell-Stammverzeichnis (mehrere Modell-Stammverzeichnisse) · es raíz de modelo (más de una raíz de modelo) · ru корневая папка моделей (несколько корневых папок моделей) · he שורש מודלים (יותר משורש מודלים אחד) |
+
+`{count}` / `{total}` / `{failed}` / `{excluded}` / `{name}` are verbatim §1-R2 placeholders in
+`deleteFolderModal.confirmMulti`, `deleteFolderResult.successMulti` / `.partial` and
+`folderRoot.notEmptyStatus` / `.notEmptyExcludedStatus`. The row verdicts are **fragments, not
+sentences**: they sit under a path inside the chooser box, so no locale capitalizes them or adds
+a period (`de` keeps its lowercase start, `fr` too). `folderRoot.rootsHint` ends with each
+locale's colon (`：` for CJK, ASCII elsewhere). `partial` reuses the locale's "N of M" shape and
+keeps the `—` before the failed count; `successMulti` keeps the locale's plain
+`deleteFolderResult.success` verb and appends the root count.
+
 ### Settings Organization tab
 
 The settings modal's fourth nav tab groups everything about how files are arranged on