feat(ai): menu @ instantane, selecteurs agrandis et BooksLM racine (#82)

Nouvel endpoint GET /api/vault/{vault}/paths + prechargement et filtrage client du menu @ (affichage instantane des fichiers/repertoires). Selecteurs Fournisseur/Modele agrandis (0,8rem / 34px) pour s'aligner sur le reste du site. Ajout de BooksLM au menu contextuel de la racine des vaults.

backend/services/search.py

@@ -113,3 +113,32 @@ def search_paths(q: str, vault: str = "all") -> dict[str, Any]:
                 })
 
     return {"query": q, "vault_filter": vault, "results": results}
+
+
+def list_paths(vault: str, limit: int = 5000) -> dict[str, Any]:
+    """Return a flat, capped list of every indexed path in a vault.
+
+    Backs the AI assistant ``@`` mention menu: fetching the whole path index
+    once lets the client filter files/directories instantly instead of issuing
+    a request per keystroke.
+
+    Args:
+        vault: Vault name.
+        limit: Maximum number of entries returned.
+
+    Returns:
+        ``{"vault", "count", "results": [{vault, path, name, type}]}``.
+    """
+    from backend.indexer import path_index
+
+    entries = path_index.get(vault, [])
+    results = [
+        {
+            "vault": vault,
+            "path": entry["path"],
+            "name": entry["name"],
+            "type": entry["type"],
+        }
+        for entry in entries[: max(0, limit)]
+    ]
+    return {"vault": vault, "count": len(results), "results": results}