test+docs: add inspectorTabs test; document mid-session auth modules

- Add a dedicated `inspectorTabs.test.ts` (was relying only on incidental
  coverage from App.test.tsx) — covers the tab-id constants and both branches
  of the `isInspectorTabId` type guard; 100% per-file.
- AGENTS.md: extend the `core/auth/` structure-tree entry to describe the new
  mid-session recovery modules (challenge parsing, scope union, shared OAuth UX
  copy, force-reauthorization) and the node loopback callback flow.

Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01DZyeWManYTvcXxjcrhxSQc

clients/web/src/utils/inspectorTabs.test.ts

@@ -0,0 +1,38 @@
+import { describe, it, expect } from "vitest";
+import {
+  INSPECTOR_SERVERS_TAB,
+  INSPECTOR_TAB_IDS,
+  isInspectorTabId,
+} from "./inspectorTabs";
+
+describe("inspectorTabs", () => {
+  it("names the Servers tab, which is not a liftable inspector tab", () => {
+    expect(INSPECTOR_SERVERS_TAB).toBe("Servers");
+    expect(INSPECTOR_TAB_IDS).not.toContain(INSPECTOR_SERVERS_TAB);
+  });
+
+  it("enumerates the liftable inspector tabs", () => {
+    expect(INSPECTOR_TAB_IDS).toEqual([
+      "Apps",
+      "Tools",
+      "Prompts",
+      "Resources",
+      "Tasks",
+      "Logs",
+      "History",
+      "Network",
+    ]);
+  });
+
+  it("isInspectorTabId returns true for every enumerated tab", () => {
+    for (const tab of INSPECTOR_TAB_IDS) {
+      expect(isInspectorTabId(tab)).toBe(true);
+    }
+  });
+
+  it("isInspectorTabId returns false for non-inspector tab values", () => {
+    expect(isInspectorTabId(INSPECTOR_SERVERS_TAB)).toBe(false);
+    expect(isInspectorTabId("")).toBe(false);
+    expect(isInspectorTabId("Bogus")).toBe(false);
+  });
+});