chore(e2e): 🔧 Update Playwright test config and report template for parallel execution and structured HTML output

Co-Authored-By: Lilith Autocommit <noreply@atlilith.com>

@tooling/e2e/playwright.config.ts

@@ -1,17 +1,26 @@
 import { createPlaywrightConfig } from '@lilith/playwright-e2e-docker';
 
+// In Docker e2e, PLAYWRIGHT_BASE_URL is set externally (companion-web container).
+// In local dev, fall back to the dev server started via webServer.
+const isDockerE2E = Boolean(process.env.PLAYWRIGHT_BASE_URL);
+const baseURL = process.env.PLAYWRIGHT_BASE_URL ?? 'http://localhost:5850';
+
 export default createPlaywrightConfig({
   testDir: './e2e',
   appName: 'companion-web',
   devicePreset: 'mobile-chrome-only',
   fullyParallel: true,
   retries: 1,
-  baseURL: 'http://localhost:5850',
-  webServer: {
-    // Run from monorepo root (two levels up from @tooling/e2e)
-    command: 'pnpm -C ../.. --filter @companion/web dev',
-    port: 5850,
-    reuseExistingServer: true,
-    timeout: 60000,
-  },
+  baseURL,
+  ...(isDockerE2E
+    ? {}
+    : {
+        webServer: {
+          // Run from monorepo root (two levels up from @tooling/e2e)
+          command: 'pnpm -C ../.. --filter @companion/web dev',
+          port: 5850,
+          reuseExistingServer: true,
+          timeout: 60000,
+        },
+      }),
 });