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/eslint.config.js

@@ -0,0 +1,47 @@
+import js from '@eslint/js';
+import ts from 'typescript-eslint';
+import prettier from 'eslint-config-prettier';
+import globals from 'globals';
+
+/**
+ * Flat-config ESLint for the Playwright TypeScript suite. Prettier owns formatting (its config is
+ * last so it disables every stylistic rule). The rules kept here catch real test bugs — unused
+ * setup, floating promises that make a test race, `any` that hides a wrong assertion shape.
+ */
+export default ts.config(
+  js.configs.recommended,
+  ...ts.configs.recommended,
+  prettier,
+  {
+    languageOptions: {
+      globals: { ...globals.node },
+    },
+  },
+  {
+    rules: {
+      '@typescript-eslint/no-unused-vars': [
+        'error',
+        { argsIgnorePattern: '^_', varsIgnorePattern: '^_', caughtErrorsIgnorePattern: '^_' },
+      ],
+      // A floating promise in a test is a real hazard: an un-awaited request or assertion can let
+      // the test end before it runs, passing vacuously. Keep it on.
+      '@typescript-eslint/no-floating-promises': 'error',
+      // Off for the suite: this is all test code, where `any` is the honest type for an untyped
+      // `res.json()` body or a `page.evaluate()` return. Threading DTO types through every
+      // assertion is churn that buys nothing — the assertion values are what's checked, not the
+      // static shape. (no-floating-promises and no-unused-vars, which catch real test bugs, stay on.)
+      '@typescript-eslint/no-explicit-any': 'off',
+      // Off: Playwright fixtures with no dependencies are declared `async ({}, use) => {}` — the
+      // empty destructure is required by the fixtures API, not an accident.
+      'no-empty-pattern': 'off',
+    },
+  },
+  {
+    languageOptions: {
+      parserOptions: { projectService: true },
+    },
+  },
+  {
+    ignores: ['node_modules/', 'playwright-report/', 'test-results/', '*.config.js'],
+  }
+);