docs: Use defineRouting in routing docs consistently

docs/pages/docs/routing.mdx

@@ -34,7 +34,7 @@ export const routing = defineRouting({
 });
 ```
 
-Depending on your routing needs, you may wish to consider further settings.
+Depending on your routing needs, you may wish to consider further settings—see below.
 
 <Details id="locales-unknown">
 <summary>What if the locales aren't known at build time?</summary>
@@ -460,22 +460,20 @@ The middleware will [detect a matching locale](/docs/routing/middleware#locale-d
 
 If you want to rely entirely on the URL to resolve the locale, you can set the `localeDetection` property to `false`. This will disable locale detection based on the `accept-language` header and a potentially existing cookie value from a previous visit.
 
-```tsx filename="middleware.ts" {5}
-import createMiddleware from 'next-intl/middleware';
-import {routing} from './i18n/routing';
+```tsx filename="routing.ts" {5}
+import {defineRouting} from 'next-intl/routing';
 
-export default createMiddleware(routing, {
+export const routing = defineRouting({
+  // ...
   localeDetection: false
 });
 ```
 
-In this case, only the locale prefix and a potentially [matching domain](#domain-based-routing) are used to determine the locale.
-
-Note that by setting this option, the middleware will no longer return a `set-cookie` response header, which can be beneficial for CDN caching (see e.g. [the Cloudflare Cache rules for `set-cookie`](https://developers.cloudflare.com/cache/concepts/cache-behavior/#interaction-of-set-cookie-response-header-with-cache)).
+In this case, only the locale prefix and a potentially [matching domain](#domains) are used to determine the locale.
 
 ### Locale cookie [#locale-cookie]
 
-By default, the middleware will set a cookie called `NEXT_LOCALE` that contains the most recently detected locale. This is used to remember the user's locale preference for future requests (see [locale detection in the middleware](/docs/routing/middleware#locale-detection)).
+By default, the middleware will set a cookie called `NEXT_LOCALE` that contains the most recently detected locale. This is used to [remember the user's locale](/docs/routing/middleware#locale-detection) preference for future requests.
 
 By default, the cookie will be configured with the following attributes:
 
@@ -485,12 +483,13 @@ By default, the cookie will be configured with the following attributes:
 
 If you have more specific requirements, you can adjust these settings accordingly:
 
-```tsx filename="middleware.ts"
-import createMiddleware from 'next-intl/middleware';
-import {routing} from './i18n/routing';
+```tsx filename="routing.ts"
+import {defineRouting} from 'next-intl/routing';
+
+export const routing = defineRouting({
+  // ...
 
-export default createMiddleware(routing, {
-  // These options will be merged with the defaults
+  // Will be merged with the defaults
   localeCookie: {
     // Custom cookie name
     name: 'USER_LOCALE',
@@ -502,16 +501,17 @@ export default createMiddleware(routing, {
 
 … or turn the cookie off entirely:
 
-```tsx filename="middleware.ts"
-import createMiddleware from 'next-intl/middleware';
-import {routing} from './i18n/routing';
+```tsx filename="routing.ts"
+import {defineRouting} from 'next-intl/routing';
+
+export const routing = defineRouting({
+  // ...
 
-export default createMiddleware(routing, {
   localeCookie: false
 });
 ```
 
-Note that the cookie is only set once per detected locale and is not updated on every request.
+Note that the cookie is only set when the user switches the locale and is not updated on every request.
 
 ### Alternate links [#alternate-links]
 
@@ -524,12 +524,13 @@ However, there are cases where you may want to provide these links yourself:
 
 In this case, you can opt-out of this behavior by setting `alternateLinks` to `false`.
 
-```tsx filename="middleware.ts" {5}
-import createMiddleware from 'next-intl/middleware';
-import {routing} from './i18n/routing';
+```tsx filename="routing.ts"
+import {defineRouting} from 'next-intl/routing';
+
+export const routing = defineRouting({
+  // ...
 
-export default createMiddleware(routing, {
-  alternateLinks: false // Defaults to `true`
+  alternateLinks: false
 });
 ```