test(website): fix the e2e main broke, and drop the obsolete next-env wrapper (#870)

Two related repairs to the website e2e lane:

1. Docs search spec: #865's a11y pass gave search results role="option",
   and an explicit ARIA role overrides the implicit button role — so
   getByRole('button') stopped matching and main's website e2e has been red
   since. The spec now queries role 'option'. (Verified the failure
   reproduces identically on pristine main before touching anything.)

2. run-e2e-with-next-env-restore.ts existed to rewrite next-env.d.ts to
   canonical content after e2e, protecting a then-tracked file from dirty-
   tree churn. #862 untracked the file, and the dangling dev-path content
   the wrapper guarded against breaks nothing today — verified by writing
   that exact content with the referenced path absent: lint 0, test 0,
   build 0 (website has no typecheck target, and build regenerates the
   file first). The e2e target now runs the playwright executor directly;
   the wrapper and its extra target indirection are gone.

Website e2e: 49/49 with the folded target.

Co-authored-by: Claude Opus 5 <noreply@anthropic.com>

Author: blove

apps/website/e2e/docs.spec.ts

@@ -147,7 +147,9 @@ test.describe('Docs search', () => {
     const searchInput = page.locator('input[placeholder*="Search"], input[type="search"]').first();
     await searchInput.fill('choosing adapter');
 
-    await expect(page.getByRole('button', { name: /Choosing an adapter/i })).toBeVisible();
+    // Search results are role="option" inside the listbox (a11y pass, #865) —
+    // an explicit ARIA role overrides the implicit button role.
+    await expect(page.getByRole('option', { name: /Choosing an adapter/i })).toBeVisible();
     await expect(page.getByText('No results found')).toHaveCount(0);
   });
 });

apps/website/project.json

@@ -70,12 +70,6 @@
       }
     },
     "e2e": {
-      "executor": "nx:run-commands",
-      "options": {
-        "command": "npx tsx apps/website/scripts/run-e2e-with-next-env-restore.ts -- npx nx run website:e2e-playwright --skip-nx-cache"
-      }
-    },
-    "e2e-playwright": {
       "executor": "@nx/playwright:playwright",
       "options": {
         "config": "apps/website/playwright.config.ts"