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/09-mobile/focus-trap.spec.ts

@@ -34,18 +34,25 @@ test.describe('Mobile a11y — focus trap on LightboxModal', () => {
     await trigger.click();
 
     // Lightbox is role="dialog" aria-modal="true".
-    const lightbox = page.locator('[role="dialog"][aria-modal="true"]').filter({ has: page.locator('img, video') });
+    const lightbox = page
+      .locator('[role="dialog"][aria-modal="true"]')
+      .filter({ has: page.locator('img, video') });
     await expect(lightbox).toBeVisible();
 
     // After opening, focus should be inside the lightbox (trap autoFocus moves
     // focus to the first focusable). Verify by checking activeElement is
     // contained.
-    await expect.poll(async () => {
-      return await page.evaluate(() => {
-        const dlg = document.querySelector('[role="dialog"][aria-modal="true"]');
-        return !!dlg && dlg.contains(document.activeElement);
-      });
-    }, { timeout: 2_000 }).toBe(true);
+    await expect
+      .poll(
+        async () => {
+          return await page.evaluate(() => {
+            const dlg = document.querySelector('[role="dialog"][aria-modal="true"]');
+            return !!dlg && dlg.contains(document.activeElement);
+          });
+        },
+        { timeout: 2_000 }
+      )
+      .toBe(true);
 
     // Escape dismisses the lightbox.
     await page.keyboard.press('Escape');