chore(e2e): add ESLint + Prettier; fix real findings; dedupe BASE

The Playwright suite had no linter and no formatter — only tsc. Add flat-config ESLint
(typescript-eslint, type-aware) and Prettier (2-space, matching the suite's style).

Rules keep the ones that catch real TEST bugs and drop the noise:
  - no-floating-promises KEPT — an un-awaited request/assertion can let a test end before it runs,
    passing vacuously. It caught one: the SSE reader loop in sse-listener is now explicitly `void`.
  - no-unused-vars KEPT — caught three dead bindings (an unused adminToken fixture arg, an unused
    `api` arg, an unused JPEG_MAGIC import), all removed.
  - no-explicit-any OFF — all test code; `any` is the honest type for an untyped res.json() body or
    a page.evaluate() return.
  - no-empty-pattern OFF — Playwright's dependency-free fixtures are `async ({}, use) => {}`.

Refactor: `const BASE = process.env.E2E_FRONTEND_URL ?? '...'` was redeclared verbatim in 23
files — extracted to helpers/env.ts and imported, so a port/scheme change is one edit not a sweep.

Then `prettier --write`. Verified: eslint clean, tsc clean, prettier clean, desktop suite 210
passed / 1 skipped. (One mobile spec flaked once under retries:0 — a pre-existing cross-test
reflow-timing vector from the flakiness audit, not this change: the each-key edit is stable across
16 isolated runs and a clean full mobile re-run.)

Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>

e2e/specs/01-auth/pin-auto-submit.spec.ts

@@ -13,7 +13,10 @@ import { JoinPage, RecoverPage } from '../../page-objects';
 import { clearAllStorage } from '../../helpers/storage-helpers';
 
 test.describe('Auth — PIN auto-submit', () => {
-  test('inline recovery: 4th digit auto-submits and navigates to /feed', async ({ page, guest }) => {
+  test('inline recovery: 4th digit auto-submits and navigates to /feed', async ({
+    page,
+    guest,
+  }) => {
     const original = await guest('AutoInline');
     await clearAllStorage(page);
 
@@ -30,7 +33,10 @@ test.describe('Auth — PIN auto-submit', () => {
     await page.waitForURL('**/feed', { timeout: 5_000 });
   });
 
-  test('/recover: 4th digit auto-submits when the name is already filled in', async ({ page, guest }) => {
+  test('/recover: 4th digit auto-submits when the name is already filled in', async ({
+    page,
+    guest,
+  }) => {
     const original = await guest('AutoRecover');
     await clearAllStorage(page);