chore(web): move App.tsx's module-level block into files (#2127)

Phase 0 of #2126. Lines 239-668 of clients/web/src/App.tsx were already at
module scope — helpers, formatters, constants, and the toast subcomponents,
none of which close over component state — so the whole block moves verbatim
into files. App.tsx drops from 5,303 to 4,892 lines with no behavior change.

Placement follows the lib-vs-utils rule in AGENTS.md: pure computation to
utils/, anything touching the environment to lib/.

EMPTY_SETTINGS and the two loose toast ids deliberately do NOT land in a new
top-level src/constants.ts, which the issue suggested: the web coverage
include is a whitelist naming components/hooks/theme/lib/utils/server, so a
module there would have fallen out of the >=90 gate silently. They go under
utils/ instead.

ReAuthBannerBar is in the block but not in the issue's table — it was added
after the issue was written (#2108). It moves to components/groups/ReAuthBanner/,
beside the banner it wraps.

Every new module is at 100% on all four coverage dimensions. Two v8 ignores,
each justified in place: getAuthToken's typeof-window guard (a happy-dom
inherent path) and replayProtocolRequest's provably-dead default case.

Signed-off-by: cliffhall <cliff@futurescale.com>

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

@@ -0,0 +1,28 @@
+import { describe, expect, it } from "vitest";
+import {
+  DEFAULT_MAX_FETCH_REQUESTS,
+  DEFAULT_TASK_TTL_MS,
+} from "@inspector/core/mcp/types.js";
+import { EMPTY_SETTINGS } from "./serverSettingsDefaults";
+
+describe("EMPTY_SETTINGS", () => {
+  it("is an empty draft carrying the shared defaults", () => {
+    expect(EMPTY_SETTINGS).toEqual({
+      headers: [],
+      env: [],
+      metadata: {},
+      connectionTimeout: 0,
+      requestTimeout: 0,
+      taskTtl: DEFAULT_TASK_TTL_MS,
+      autoRefreshOnListChanged: false,
+      paginatedLists: false,
+      maxFetchRequests: DEFAULT_MAX_FETCH_REQUESTS,
+      roots: [],
+    });
+  });
+
+  it("keeps one object identity so React sees a stable reference", async () => {
+    const again = await import("./serverSettingsDefaults");
+    expect(again.EMPTY_SETTINGS).toBe(EMPTY_SETTINGS);
+  });
+});