fix(next): update rest route handler types for Next.js 15.5 compatibility (#13521)

Fixes #13527.

When upgrading to [Next.js 15.5](https://nextjs.org/blog/next-15-5) with
Payload, you might experience a runtime or build error similar to this:

```ts
Type error: Type 'typeof import("/src/app/(payload)/api/graphql/route")' does not satisfy the expected type 'RouteHandlerConfig<"/api/graphql">'.
  Types of property 'OPTIONS' are incompatible.
    Type '(request: Request, args: { params: Promise<{ slug: string[]; }>; }) => Promise<Response>' is not assignable to type '(request: NextRequest, context: { params: Promise<{}>; }) => void | Promise<void> | Response | Promise<Response>'.
      Types of parameters 'args' and 'context' are incompatible.
        Type '{ params: Promise<{}>; }' is not assignable to type '{ params: Promise<{ slug: string[]; }>; }'.
          Types of property 'params' are incompatible.
            Type 'Promise<{}>' is not assignable to type 'Promise<{ slug: string[]; }>'.
              Property 'slug' is missing in type '{}' but required in type '{ slug: string[]; }'.
```

This is because Next.js route types are now _stricter_. Our REST handler
is nested within a catch-all `/api/[...slug]` route, so the slug param
_will_ exist in the handler—but the _same_ handler is re-used for the
`/api/graphql` OPTIONS route, which **_is not_** nested within the
`slug` param and so it **_will not_** exist as the types suggest.

---
- To see the specific tasks where the Asana app for GitHub is being
used, see below:
  - https://app.asana.com/0/0/1211115021865680

---------

Co-authored-by: Jacob Fletcher <jacobsfletch@gmail.com>

packages/next/src/routes/rest/index.ts

@@ -9,7 +9,7 @@ const handlerBuilder =
   async (
     request: Request,
     args: {
-      params: Promise<{ slug: string[] }>
+      params: Promise<{ slug?: string[] }>
     },
   ): Promise<Response> => {
     const awaitedConfig = await config

templates/website/src/app/(frontend)/next/preview/route.ts

@@ -3,18 +3,11 @@ import { getPayload } from 'payload'
 
 import { draftMode } from 'next/headers'
 import { redirect } from 'next/navigation'
+import { NextRequest } from "next/server"
 
 import configPromise from '@payload-config'
 
-export async function GET(
-  req: {
-    cookies: {
-      get: (name: string) => {
-        value: string
-      }
-    }
-  } & Request,
-): Promise<Response> {
+export async function GET(req: NextRequest): Promise<Response> {
   const payload = await getPayload({ config: configPromise })
 
   const { searchParams } = new URL(req.url)

templates/with-vercel-website/src/app/(frontend)/next/preview/route.ts

@@ -3,18 +3,11 @@ import { getPayload } from 'payload'
 
 import { draftMode } from 'next/headers'
 import { redirect } from 'next/navigation'
+import { NextRequest } from "next/server"
 
 import configPromise from '@payload-config'
 
-export async function GET(
-  req: {
-    cookies: {
-      get: (name: string) => {
-        value: string
-      }
-    }
-  } & Request,
-): Promise<Response> {
+export async function GET(req: NextRequest): Promise<Response> {
   const payload = await getPayload({ config: configPromise })
 
   const { searchParams } = new URL(req.url)