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/errorFormat.test.ts

@@ -0,0 +1,66 @@
+import { describe, expect, it } from "vitest";
+import { errorCodeOf, errorMessage, formatErrorDetails } from "./errorFormat";
+
+describe("errorMessage", () => {
+  it("returns an Error's message", () => {
+    expect(errorMessage(new Error("boom"))).toBe("boom");
+  });
+
+  it("stringifies a non-Error", () => {
+    expect(errorMessage("plain string")).toBe("plain string");
+    expect(errorMessage(undefined)).toBe("undefined");
+    expect(errorMessage(42)).toBe("42");
+  });
+});
+
+describe("errorCodeOf", () => {
+  it("reads a numeric `code` off a protocol error", () => {
+    expect(
+      errorCodeOf(Object.assign(new Error("nope"), { code: -32602 })),
+    ).toBe(-32602);
+  });
+
+  it("returns undefined for a plain Error", () => {
+    expect(errorCodeOf(new Error("plain"))).toBeUndefined();
+  });
+
+  it("returns undefined when `code` is not a number", () => {
+    expect(errorCodeOf({ code: "-32602" })).toBeUndefined();
+  });
+
+  it("returns undefined for non-objects", () => {
+    expect(errorCodeOf(null)).toBeUndefined();
+    expect(errorCodeOf("boom")).toBeUndefined();
+  });
+});
+
+describe("formatErrorDetails", () => {
+  it("pretty-prints code/message/data when a code is present", () => {
+    const err = Object.assign(new Error("bad params"), {
+      code: -32602,
+      data: { field: "uri" },
+    });
+    expect(JSON.parse(formatErrorDetails(err))).toEqual({
+      code: -32602,
+      message: "bad params",
+      data: { field: "uri" },
+    });
+  });
+
+  it("pretty-prints when only `data` is present", () => {
+    expect(
+      JSON.parse(formatErrorDetails({ data: [1, 2], message: "m" })),
+    ).toEqual({ message: "m", data: [1, 2] });
+  });
+
+  it("falls back to the plain message for a bare Error", () => {
+    expect(formatErrorDetails(new Error("just a message"))).toBe(
+      "just a message",
+    );
+  });
+
+  it("falls back to String() for a non-object", () => {
+    expect(formatErrorDetails("boom")).toBe("boom");
+    expect(formatErrorDetails(null)).toBe("null");
+  });
+});