ci: update integration docs (#4494)

Co-authored-by: delucis <[email protected]>
Co-authored-by: Sarah Rainsberger <[email protected]>

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

@@ -120,7 +120,7 @@ From an endpoint:
 
 ```js
 // src/pages/api/someFile.js
-export function get(context) {
+export function GET(context) {
   const runtime = context.locals.runtime;
 
   return new Response('Some body');
@@ -134,7 +134,7 @@ If you're using the `advanced` runtime, you can type the `runtime` object as fol
 ```ts
 // src/env.d.ts
 /// <reference types="astro/client" />
-type AdvancedRuntime = import('@astrojs/cloudflare').AdvancedRuntime;
+import type { AdvancedRuntime } from '@astrojs/cloudflare';
 
 declare namespace App {
   interface Locals extends AdvancedRuntime {
@@ -151,7 +151,7 @@ If you're using the `directory` runtime, you can type the `runtime` object as fo
 ```ts
 // src/env.d.ts
 /// <reference types="astro/client" />
-type DirectoryRuntime = import('@astrojs/cloudflare').DirectoryRuntime;
+import type { DirectoryRuntime } from '@astrojs/cloudflare';
 
 declare namespace App {
   interface Locals extends DirectoryRuntime {

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

@@ -153,7 +153,7 @@ You can now [import your own `base.css` as a local stylesheet](/en/guides/stylin
 ## Examples
 
 *   The [Astro Tailwind Starter](https://github.com/withastro/astro/tree/latest/examples/with-tailwindcss?on=github) gets you up and running with a base for your project that uses Tailwind for styling
-*   Astro's homepage uses Tailwind. Check out its [Tailwind configuration file](https://github.com/withastro/astro.build/blob/main/tailwind.config.ts) or an [example component](https://github.com/withastro/astro.build/blob/main/src/components/Checkbox.astro)
+*   Astro's homepage uses Tailwind. Check out its [Tailwind configuration file](https://github.com/withastro/astro.build/blob/main/tailwind.config.cjs) or an [example component](https://github.com/withastro/astro.build/blob/main/src/components/Checkbox.astro)
 *   The [Astro Ink](https://github.com/one-aalam/astro-ink), [Sarissa Blog](https://github.com/iozcelik/SarissaBlogAstroStarter), and [Creek](https://github.com/robertguss/Astro-Theme-Creek) themes use Tailwind for styling
 *   [Browse Astro Tailwind projects on GitHub](https://github.com/search?q=%22%40astrojs%2Ftailwind%22%3A+path%3A%2Fpackage.json\&type=code) for more examples!
 

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

@@ -127,6 +127,8 @@ export default defineConfig({
 
 Configuration options for [Vercel's Image Optimization API](https://vercel.com/docs/concepts/image-optimization). See [Vercel's image configuration documentation](https://vercel.com/docs/build-output-api/v3/configuration#images) for a complete list of supported parameters.
 
+The `domains` and `remotePatterns` properties will automatically be filled using [the Astro corresponding `image` settings](/en/reference/configuration-reference/#image-options).
+
 ```js
 // astro.config.mjs
 import { defineConfig } from 'astro/config';