feat: update edgeMiddleware references to middlewareMode

src/content/docs/en/guides/integrations-guide/netlify.mdx

@@ -98,9 +98,9 @@ The [Netlify Blog post on Astro](https://www.netlify.com/blog/how-to-deploy-astr
 
 ### Running Astro middleware on Netlify Edge Functions
 
-Any Astro middleware is applied to pre-rendered pages at build-time, and to on-demand-rendered pages at runtime.
+By default, Astro middleware is applied to pre-rendered pages at build-time, and to on-demand-rendered pages at runtime.
 
-To implement redirects, access control, or custom response headers for pre-rendered pages, run your middleware on Netlify Edge Functions by enabling the [`edgeMiddleware` option](/en/reference/adapter-reference/#edgemiddleware):
+To implement redirects, access control, or custom response headers for pre-rendered pages, run your middleware on Netlify Edge Functions by setting the [`middlewareMode` option](/en/reference/adapter-reference/#middlewaremode) to `edge`:
 
 ```js title="astro.config.mjs" ins={7}
 import { defineConfig } from 'astro/config';
@@ -109,12 +109,12 @@ import netlify from '@astrojs/netlify';
 export default defineConfig({
   // ...
   adapter: netlify({
-    edgeMiddleware: true,
+    middlewareMode: 'edge',
   }),
 });
 ```
 
-When `edgeMiddleware` is enabled, an edge function will execute your middleware code for all requests including static assets, prerendered pages, and on-demand rendered pages.
+When `middlewareMode` is set to `'edge'`, an edge function will execute your middleware code for all requests including static assets, prerendered pages, and on-demand rendered pages.
 
 For on-demand rendered pages, the `context.locals` object is serialized using JSON and sent in a header for the serverless function, which performs the rendering. As a security measure, the serverless function will refuse to serve requests with a `403 Forbidden` response unless they come from the generated edge function.
 

src/content/docs/en/guides/integrations-guide/vercel.mdx

@@ -442,20 +442,20 @@ export default defineConfig({
 
 ### Running Astro middleware on Vercel Edge Functions
 
-The `@astrojs/vercel` adapter can create an [edge function](https://vercel.com/docs/functions/edge-functions) from an Astro middleware in your code base. When `edgeMiddleware` is enabled, an edge function will execute your middleware code for all requests including static assets, prerendered pages, and on-demand rendered pages.
+The `@astrojs/vercel` adapter can create an [edge function](https://vercel.com/docs/functions/edge-functions) from an Astro middleware in your code base. When [`middlewareMode`](/en/reference/adapter-reference/#middlewaremode) is set to `'edge'`, an edge function will execute your middleware code for all requests including static assets, prerendered pages, and on-demand rendered pages.
 
 For on-demand rendered pages, the `context.locals` object is serialized using JSON and sent in a header for the serverless function, which performs the rendering. As a security measure, the serverless function will refuse to serve requests with a `403 Forbidden` response unless they come from the generated edge function.
 
-This is an opt-in feature. To enable it, set `edgeMiddleware` to `true`:
+This is an opt-in feature. To enable it, set `middlewareMode` to `'edge'`:
 
-```js title="astro.config.mjs" "edgeMiddleware: true"
+```js title="astro.config.mjs" "middlewareMode: 'edge'"
 import { defineConfig } from 'astro/config';
 import vercel from '@astrojs/vercel';
 
 export default defineConfig({
   // ...
   adapter: vercel({
-    edgeMiddleware: true,
+    middlewareMode: 'edge',
   }),
 });
 ```

src/content/docs/en/reference/adapter-reference.mdx

@@ -1041,16 +1041,20 @@ Defines whether the adapter supports image transformation using the built-in Sha
 
 A set of features that changes the output of the emitted files. When an adapter opts in to these features, they will get additional information inside specific hooks and must implement the proper logic to handle the different output.
 
-### `edgeMiddleware`
+### `middlewareMode`
 
 <p>
 
-**Type:** `boolean`
+**Type:** [`MiddlewareMode`](#middlewaremode-1)<br />
+**Default:** `"classic"`<br />
+<Since v="6.0.0" />
 </p>
 
-Defines whether any on-demand rendering middleware code will be bundled when built.
+Determines at which stage of the page lifecycle the middleware is executed, and how the middleware code is emitted in the build output.
+
+The `classic` mode matches the default behavior of Astro. On prerendered pages, middleware is run at build time, and when the page is requested, the middleware is not run again. On dynamic pages, middleware is run at request time only. The middleware code is part of your server bundle.
 
-When enabled, this prevents middleware code from being bundled and imported by all pages during the build:
+In `edge` mode, the middleware code can be deployed independently from the server bundle, for example, as an edge function.
 
 ```js title="my-adapter.mjs" ins={10-12}
 export default function createIntegration() {
@@ -1063,7 +1067,7 @@ export default function createIntegration() {
           entrypointResolution: 'auto',
           serverEntrypoint: '@example/my-adapter/server.js',
           adapterFeatures: {
-            edgeMiddleware: true
+            middlewareMode: 'edge'
           } 
         });
       },
@@ -1085,7 +1089,7 @@ export default function createIntegration() {
           entrypointResolution: 'auto',
           serverEntrypoint: '@example/my-adapter/server.js',
           adapterFeatures: {
-            edgeMiddleware: true
+            middlewareMode: 'edge'
           } 
         });
       },
@@ -1287,6 +1291,16 @@ export default function createIntegration() {
 }
 ```
 
+### `MiddlewareMode`
+
+<p>
+
+**Type:** `"classic" | "edge"`<br />
+<Since v="6.0.0" />
+</p>
+
+A union of valid formats to describe the mode in which middleware is run.
+
 ## Allow installation via `astro add`
 
 [The `astro add` command](/en/reference/cli-reference/#astro-add) allows users to easily add integrations and adapters to their project.  To allow your adapter to be installed with this command, **add `astro-adapter` to the `keywords` field in your `package.json`**: