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/package.json

@@ -14,13 +14,23 @@
     "stack:up": "docker compose -f docker-compose.test.yml up -d --build",
     "stack:down": "docker compose -f docker-compose.test.yml down -v",
     "stack:logs": "docker compose -f docker-compose.test.yml logs -f",
-    "install:browsers": "playwright install --with-deps chromium firefox webkit"
+    "install:browsers": "playwright install --with-deps chromium firefox webkit",
+    "lint": "eslint .",
+    "lint:fix": "eslint . --fix",
+    "format": "prettier --write .",
+    "format:check": "prettier --check ."
   },
   "devDependencies": {
+    "@eslint/js": "^9.39.5",
     "@playwright/test": "^1.49.0",
     "@types/node": "^22.10.0",
-    "pg": "^8.13.1",
     "@types/pg": "^8.11.10",
-    "typescript": "^5.7.0"
+    "eslint": "^9.39.5",
+    "eslint-config-prettier": "^9.1.2",
+    "globals": "^15.15.0",
+    "pg": "^8.13.1",
+    "prettier": "^3.9.5",
+    "typescript": "^5.7.0",
+    "typescript-eslint": "^8.64.0"
   }
 }