fix(web): admin bibliothèques — correctifs complémentaires client et AdminPage

- web: AdminPage, client API (+ tests), styles

Refs: #15

apps/web/src/api/client.test.ts

@@ -1,5 +1,9 @@
-import { describe, expect, it } from "vitest";
-import { ApiFallbackError, getApiFallback } from "./client";
+import { afterEach, describe, expect, it, vi } from "vitest";
+import { api, ApiFallbackError, getApiFallback } from "./client";
+
+afterEach(() => {
+  vi.unstubAllGlobals();
+});
 
 describe("api fallback helpers", () => {
   it("extracts typed fallback payloads", () => {
@@ -9,4 +13,21 @@ describe("api fallback helpers", () => {
   it("ignores non fallback errors", () => {
     expect(getApiFallback<string[]>(new Error("boom"))).toBeUndefined();
   });
+
+  it("does not send JSON content-type for bodyless delete requests", async () => {
+    const fetchMock = vi.fn().mockResolvedValue(
+      new Response(JSON.stringify({ ok: true }), {
+        status: 200,
+        headers: { "Content-Type": "application/json" }
+      })
+    );
+    vi.stubGlobal("fetch", fetchMock);
+
+    await api.deleteLibrary(42);
+
+    const init = fetchMock.mock.calls[0][1] as RequestInit;
+    const headers = new Headers(init.headers);
+    expect(init.method).toBe("DELETE");
+    expect(headers.has("Content-Type")).toBe(false);
+  });
 });