feat(breadcrumb): build breadcrumb in 1 API call

add /api/folders/{id}/ancestors

    this API to iterate parent up to the drive root or the shared folder
    this will help UI to build the breadcrumb in 1 API call
    and to identify the root element (is it a drive users has access to or
    a shared folder ?)

    ui: now only 1 API call is now required to build the breadcrumb

frontend/src/lib/api/endpoints/folders.ts

@@ -1,7 +1,7 @@
 /** Folder endpoints — ported from filesModel.js + fileOperations.js. */
 import { apiFetch, apiJson } from '$lib/api/client';
 import { getCsrfHeaders } from '$lib/api/csrf';
-import type { FileItem, FolderItem, ItemType } from '$lib/api/types';
+import type { FileItem, FolderAncestorsResponse, FolderItem, ItemType } from '$lib/api/types';
 
 const JSON_HEADERS = { 'Content-Type': 'application/json' };
 const NO_CACHE: RequestInit = {
@@ -109,6 +109,35 @@ export function getFolder(id: string): Promise<FolderItem> {
 	return request;
 }
 
+// ── Ancestor chain (breadcrumb) ──────────────────────────────────────────
+// Backing store + inflight dedup for `GET /api/folders/{id}/ancestors` —
+// mirrors the folderInflight pattern for `getFolder`. Rapid navigation
+// (files → sub → sub-sub in <1s) folds concurrent requests for the same
+// leaf into one round-trip. Response also seeds `folderNames` for every
+// ancestor, so subsequent `getFolderName(id)` lookups are cache-free.
+const ancestorsInflight = new Map<string, Promise<FolderAncestorsResponse>>();
+
+export function getFolderAncestors(id: string): Promise<FolderAncestorsResponse> {
+	const inflight = ancestorsInflight.get(id);
+	if (inflight) return inflight;
+	const request = (async () => {
+		try {
+			const chain = await apiJson<FolderAncestorsResponse>(
+				`/api/folders/${id}/ancestors`,
+				NO_CACHE
+			);
+			// Prime the shared folder-name cache — the breadcrumb walk
+			// happens to be the exact input that populates it.
+			for (const a of chain.ancestors) rememberFolderName(a.id, a.name);
+			return chain;
+		} finally {
+			ancestorsInflight.delete(id);
+		}
+	})();
+	ancestorsInflight.set(id, request);
+	return request;
+}
+
 /** One page of `/api/folders/{id}/resources`. */
 export interface FolderPage {
 	/**

frontend/src/lib/api/types.ts

@@ -413,3 +413,68 @@ export interface DriveMember {
 	granted_at: string;
 	expires_at?: string | null;
 }
+
+// ─── Folder ancestors (breadcrumb endpoint) ──────────────────────────────
+// Wire shape of `GET /api/folders/{id}/ancestors`. Mirrors the backend
+// `FolderAncestorsDto` — see `src/application/dtos/folder_dto.rs`. One
+// round-trip returns the whole caller-visible parent chain plus an
+// `access_source` telling the breadcrumb component which root icon /
+// tooltip to render.
+
+export interface FolderAncestor {
+	id: string;
+	name: string;
+	/** `null` on the drive-root ancestor. */
+	parent_id: string | null;
+	/**
+	 * Drive the folder belongs to (always populated — every folder has a
+	 * drive_id post-D0). Lets `/files` derive `currentFolderDriveId` from
+	 * the ancestors response instead of firing an extra
+	 * `GET /api/folders/{id}` on load. Same value across every entry in
+	 * `ancestors` (all folders in a chain live in one drive).
+	 */
+	drive_id: string;
+}
+
+/**
+ * How the caller reached the topmost accessible ancestor.
+ * - `drive` — via drive membership (own personal, secondary personal, or
+ *   shared drive). `drive` field carries the drive's id/name/kind for
+ *   the root icon.
+ * - `direct_share` — via a folder-level `role_grants` row (share).
+ *   `subject` may name the grantee (self or a group) once subject
+ *   enrichment lands; MVP leaves it null.
+ * - `token` — reserved for public-link callers. Not emitted today.
+ */
+export type AccessSourceKind = 'drive' | 'direct_share' | 'token';
+
+export interface AccessSourceDrive {
+	id: string;
+	name: string;
+	kind: DriveKind;
+}
+
+export interface AccessSourceSubject {
+	kind: 'user' | 'group';
+	id: string;
+	/** Nullable in MVP (subject enrichment deferred). */
+	name?: string | null;
+}
+
+export interface AccessSource {
+	kind: AccessSourceKind;
+	/** Populated when `kind === 'drive'`. */
+	drive?: AccessSourceDrive;
+	/** Optional grantee info for shares / group grants. */
+	subject?: AccessSourceSubject;
+}
+
+/**
+ * Response envelope of `GET /api/folders/{id}/ancestors`. `ancestors`
+ * is root-first, leaf-last (length ≥ 1). `access_source` describes
+ * the boundary at element 0 (drive root or share boundary).
+ */
+export interface FolderAncestorsResponse {
+	ancestors: FolderAncestor[];
+	access_source: AccessSource;
+}