chore(deps): update nextjs monorepo to v16.1.1 (#1036)

This PR contains the following updates:

| Package | Type | Update | Change | OpenSSF |
|---|---|---|---|---|
| [@next/third-parties](https://redirect.github.com/vercel/next.js)
([source](https://redirect.github.com/vercel/next.js/tree/HEAD/packages/third-parties))
| dependencies | patch | [`16.1.0` ->
`16.1.1`](https://renovatebot.com/diffs/npm/@next%2fthird-parties/16.1.0/16.1.1)
| [![OpenSSF
Scorecard](https://api.securityscorecards.dev/projects/github.com/vercel/next.js/badge)](https://securityscorecards.dev/viewer/?uri=github.com/vercel/next.js)
|
|
[eslint-config-next](https://nextjs.org/docs/app/api-reference/config/eslint)
([source](https://redirect.github.com/vercel/next.js/tree/HEAD/packages/eslint-config-next))
| devDependencies | patch | [`16.1.0` ->
`16.1.1`](https://renovatebot.com/diffs/npm/eslint-config-next/16.1.0/16.1.1)
| [![OpenSSF
Scorecard](https://api.securityscorecards.dev/projects/github.com/vercel/next.js/badge)](https://securityscorecards.dev/viewer/?uri=github.com/vercel/next.js)
|
| [next](https://nextjs.org)
([source](https://redirect.github.com/vercel/next.js)) | dependencies |
patch | [`16.1.0` ->
`16.1.1`](https://renovatebot.com/diffs/npm/next/16.1.0/16.1.1) |
[![OpenSSF
Scorecard](https://api.securityscorecards.dev/projects/github.com/vercel/next.js/badge)](https://securityscorecards.dev/viewer/?uri=github.com/vercel/next.js)
|

---

### Release Notes

<details>
<summary>vercel/next.js (@&#8203;next/third-parties)</summary>

###
[`v16.1.1`](https://redirect.github.com/vercel/next.js/releases/tag/v16.1.1)

[Compare
Source](https://redirect.github.com/vercel/next.js/compare/v16.1.0...v16.1.1)

> \[!NOTE]
> This release is backporting bug fixes. It does **not** include all
pending features/changes on canary.

##### Core Changes

- Turbopack: Create junction points instead of symlinks on Windows
()[#&#8203;87606](https://redirect.github.com/vercel/next.js/issues/87606))

##### Credits

Huge thanks to [@&#8203;sokra](https://redirect.github.com/sokra) and
[@&#8203;ztanner](https://redirect.github.com/ztanner) for helping!

</details>

<details>
<summary>vercel/next.js (eslint-config-next)</summary>

###
[`v16.1.1`](https://redirect.github.com/vercel/next.js/compare/v16.1.0...v16.1.1)

[Compare
Source](https://redirect.github.com/vercel/next.js/compare/v16.1.0...v16.1.1)

</details>

<details>
<summary>vercel/next.js (next)</summary>

###
[`v16.1.1`](https://redirect.github.com/vercel/next.js/compare/v16.1.0...3aa53984e9d6bc4b5860c76e90cccfd6780989af)

[Compare
Source](https://redirect.github.com/vercel/next.js/compare/v16.1.0...v16.1.1)

</details>

---

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---

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<!-- This is an auto-generated description by cubic. -->
---
## Summary by cubic
Upgrade Next.js and related packages to 16.1.1 to apply patch fixes.
Includes Turbopack’s Windows junction-point change for more reliable
local dev; no breaking changes.

- **Dependencies**
  - next: 16.1.0 → 16.1.1
  - @next/third-parties: 16.1.0 → 16.1.1
  - eslint-config-next: 16.1.0 → 16.1.1

<sup>Written for commit e336803.
Summary will update automatically on new commits.</sup>

<!-- End of auto-generated description by cubic. -->

Signed-off-by: renovate[bot] <29139614+renovate[bot]@users.noreply.github.com>
Co-authored-by: renovate[bot] <29139614+renovate[bot]@users.noreply.github.com>

Author: renovate[bot]

bun.lock

@@ -18,7 +18,7 @@
   "dependencies": {
     "@ai-sdk/openai": "2.0.88",
     "@ai-sdk/react": "2.0.118",
-    "@next/third-parties": "16.1.0",
+    "@next/third-parties": "16.1.1",
     "@radix-ui/react-accordion": "1.2.12",
     "@radix-ui/react-collapsible": "1.1.12",
     "@radix-ui/react-presence": "1.1.5",
@@ -41,7 +41,7 @@
     "hast-util-to-jsx-runtime": "2.3.6",
     "lucide-react": "0.562.0",
     "mermaid": "11.12.2",
-    "next": "16.1.0",
+    "next": "16.1.1",
     "next-validate-link": "1.6.3",
     "posthog-js": "1.309.1",
     "react": "19.2.3",
@@ -64,7 +64,7 @@
     "postcss": "8.5.6",
     "tailwindcss": "4.1.18",
     "typescript": "5.9.3",
-    "eslint-config-next": "16.1.0",
+    "eslint-config-next": "16.1.1",
     "eslint": "9.39.2",
     "@eslint/eslintrc": "3.3.3",
     "prettier": "3.7.4"