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/helpers/sse.ts

@@ -4,8 +4,7 @@
  * it lives in one place instead of being re-inlined per spec.
  */
 import type { Page } from '@playwright/test';
-
-const BASE = process.env.E2E_FRONTEND_URL ?? 'http://localhost:3101';
+import { BASE } from './env';
 
 /** Exchange a JWT for a single-use SSE ticket via POST /api/v1/stream/ticket. */
 export async function mintSseTicket(jwt: string): Promise<string> {
@@ -13,7 +12,8 @@ export async function mintSseTicket(jwt: string): Promise<string> {
     method: 'POST',
     headers: { Authorization: `Bearer ${jwt}` },
   });
-  if (res.status !== 200) throw new Error(`mintSseTicket failed: ${res.status} ${await res.text()}`);
+  if (res.status !== 200)
+    throw new Error(`mintSseTicket failed: ${res.status} ${await res.text()}`);
   return (await res.json()).ticket;
 }