chore(examples): Remove spare dependencies from basic example. (#9516)

### Description

I left some unneeded dependencies behind when I was upgrading this
example in #9501. This gets rid of them.

### Testing Instructions

I've verified that ESLint violations get reported as expected in my
editor and when running `turbo lint`. You can also clone with `npx
create-turbo@canary -e
https://github.com/vercel/turborepo/tree/shew-0f804/examples/basic
basic-eslint-9` to have a play with it.

examples/basic/apps/docs/package.json

@@ -22,8 +22,6 @@
     "@types/node": "^20",
     "@types/react": "18.3.1",
     "@types/react-dom": "18.3.0",
-    "eslint": "^9.15.0",
-    "eslint-config-next": "15.0.3",
     "typescript": "5.5.4"
   }
 }

examples/basic/apps/web/package.json

@@ -22,8 +22,6 @@
     "@types/node": "^20",
     "@types/react": "18.3.1",
     "@types/react-dom": "18.3.0",
-    "eslint": "^9.15.0",
-    "eslint-config-next": "15.0.3",
     "typescript": "5.5.4"
   }
 }

examples/basic/package.json

@@ -12,7 +12,7 @@
     "turbo": "^2.3.0",
     "typescript": "5.5.4"
   },
-  "packageManager": "pnpm@8.15.6",
+  "packageManager": "pnpm@9.0.0",
   "engines": {
     "node": ">=18"
   }

examples/basic/packages/eslint-config/next.js

@@ -8,7 +8,7 @@ import pluginNext from "@next/eslint-plugin-next";
 import { config as baseConfig } from "./base.js";
 
 /**
- * A custom ESLint configuration for libraries that use React.
+ * A custom ESLint configuration for libraries that use Next.js.
  *
  * @type {import("eslint").Linter.Config}
  * */

examples/basic/packages/ui/package.json

@@ -17,11 +17,9 @@
     "@repo/eslint-config": "workspace:*",
     "@repo/typescript-config": "workspace:*",
     "@turbo/gen": "^1.12.4",
-    "@types/eslint": "^8.56.5",
     "@types/node": "^20.11.24",
     "@types/react": "18.3.0",
     "@types/react-dom": "18.3.1",
-    "eslint": "^9.15.0",
     "typescript": "5.5.4"
   },
   "dependencies": {