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/back-chevron.spec.ts

@@ -6,7 +6,9 @@
 import { test, expect } from '../../fixtures/test';
 
 test.describe('Navigation — back chevrons', () => {
-  test('/recover back chevron navigates to /feed (which redirects to /join when unauth)', async ({ page }) => {
+  test('/recover back chevron navigates to /feed (which redirects to /join when unauth)', async ({
+    page,
+  }) => {
     await page.goto('/recover');
     const back = page.getByTestId('recover-back');
     await expect(back).toBeVisible();
@@ -15,7 +17,11 @@ test.describe('Navigation — back chevrons', () => {
     await page.waitForURL(/\/(join|feed)$/);
   });
 
-  test('/export back chevron returns the authenticated guest to /feed', async ({ page, guest, signIn }) => {
+  test('/export back chevron returns the authenticated guest to /feed', async ({
+    page,
+    guest,
+    signIn,
+  }) => {
     const g = await guest('ExportBack');
     await signIn(page, g);
     await page.goto('/export');