chore(docs): align Next.js quickstart demo with monorepo catalog (#47144)

## I have read the CONTRIBUTING.md file.
YES

## What kind of change does this PR introduce?
Docs update, example maintenance

Closes DOCS-362.

## What is the current behavior?
- Linear item: Next JS checks (DOCS-362)
- `@supabase/ssr: "latest"` and unpinned `next` in
nextjs-user-management
- Duplicate `next.config.js` + `next.config.ts`
- Auth quickstart linked to non-existent
`/guides/auth/server-side/nextjs`

## What is the new behavior?
- Pinned `next@16.2.6`, `@supabase/ssr@0.10.2` per monorepo catalog
- Removed duplicate `next.config.js`
- Auth quickstart links to `creating-a-client?framework=nextjs`
- Audit skills moved to
[supabase/docs-agent-skills](https://github.com/supabase/docs-agent-skills):
[`audit-nextjs-docs`](https://github.com/supabase/docs-agent-skills/blob/main/.claude/skills/audit-nextjs-docs/SKILL.md),
[`audit-quickstarts`](https://github.com/supabase/docs-agent-skills/blob/main/.claude/skills/audit-quickstarts/SKILL.md)

## Additional context
- Verification (author): `npm install && npm run build` in
nextjs-user-management — **pass** (Next.js 16.2.6)
- Skill audit: no stale `middleware.ts` in Next docs paths; broken link
fixed; duplicate config removed

| Check | Result |
|-------|--------|
| Version matrix | Pass (pinned to catalog) |
| proxy.ts / no middleware refs | Pass |
| nextjs-user-management build | Pass |
| Auth quickstart link | Fixed |

### Test plan
- [ ] `cd examples/user-management/nextjs-user-management && npm install
&& npm run build`
- [ ] `cd apps/docs && pnpm codegen:examples && pnpm lint:mdx` on
changed MDX
- [ ] Framework quickstart — `create-next-app -e with-supabase` and
publishable key env vars
- [ ] Auth quickstart — "Learn more" resolves (no 404)
- [ ] Web app tutorial — code samples use `proxy.ts`
- [ ] Start nextjs-user-management locally with `.env.local` —
login/account flow
- [ ] Install audit skills from
[docs-agent-skills](https://github.com/supabase/docs-agent-skills) (`ln
-sf ~/GitHub/supabase/docs-agent-skills/.claude/skills/audit-nextjs-docs
~/.claude/skills/audit-nextjs-docs` and same for `audit-quickstarts`),
then run checklists in
[audit-nextjs-docs](https://github.com/supabase/docs-agent-skills/blob/main/.claude/skills/audit-nextjs-docs/SKILL.md)
and
[audit-quickstarts](https://github.com/supabase/docs-agent-skills/blob/main/.claude/skills/audit-quickstarts/SKILL.md)

<!-- This is an auto-generated comment: release notes by coderabbit.ai
-->

## Summary by CodeRabbit

* **Documentation**
* Updated resource links in authentication quickstart guides for
improved navigation.

* **Chores**
* Updated dependencies in the Next.js user management example to latest
stable versions.
  * Removed unused configuration settings from the example application.

<!-- end of auto-generated comment: release notes by coderabbit.ai -->

---------

Co-authored-by: Nik Richers <nik@validmind.ai>

apps/docs/content/guides/auth/quickstarts/nextjs.mdx

@@ -95,5 +95,5 @@ hideToc: true
 
 ## Learn more
 
-- [Setting up Server-Side Auth for Next.js](/docs/guides/auth/server-side/nextjs) for a Next.js deep dive
+- [Setting up Server-Side Auth for Next.js](/docs/guides/auth/server-side/creating-a-client?queryGroups=framework&framework=nextjs) for a Next.js deep dive
 - [Supabase Auth docs](/docs/guides/auth#authentication) for more Supabase authentication methods

examples/user-management/nextjs-user-management/next.config.js

@@ -1,4 +0,0 @@
-/** @type {import('next').NextConfig} */
-const nextConfig = {}
-
-module.exports = nextConfig

examples/user-management/nextjs-user-management/package.json

@@ -9,9 +9,9 @@
     "lint": "next lint"
   },
   "dependencies": {
-    "@supabase/ssr": "latest",
+    "@supabase/ssr": "0.10.2",
     "@supabase/supabase-js": "^2",
-    "next": "^16.2.1",
+    "next": "16.2.6",
     "react": "^19.2.4",
     "react-dom": "^19.2.4"
   },