Update deployment docs to fix oversized image. (#33934)

We made the images expand to fit the full width of the container, but the deploy button image shouldn't be that large. Also made some slight refactors here to improve on my past documentation changes.

docs/deployment.md

@@ -28,9 +28,9 @@ All JavaScript code inside `.next` has been **compiled** and browser bundles hav
 
 ## Managed Next.js with Vercel
 
-[Vercel](https://vercel.com/) is a frontend cloud platform from the creators of Next.js. It's the fastest way to deploy your managed Next.js application with zero configuration.
+[Vercel](https://vercel.com?utm_source=github.com&utm_medium=referral&utm_campaign=deployment) is the fastest way to deploy your Next.js application with zero configuration.
 
-When deploying to Vercel, the platform automatically detects Next.js, runs `next build`, and optimizes the build output for you, including:
+When deploying to Vercel, the platform [automatically detects Next.js](https://vercel.com/solutions/nextjs?utm_source=github.com&utm_medium=referral&utm_campaign=deployment), runs `next build`, and optimizes the build output for you, including:
 
 - Persisting cached assets across deployments if unchanged
 - [Immutable deployments](https://vercel.com/features/previews) with a unique URL for every commit
@@ -49,9 +49,7 @@ In addition, Vercel provides features like:
 - Support for [Image Optimization](/docs/basic-features/image-optimization.md) with `next/image`
 - Instant global deployments via `git push`
 
-You can start using Vercel (for free) through a personal hobby account, or create a team to start the next big thing. Learn more about [Next.js on Vercel](https://vercel.com/solutions/nextjs) or read the [Vercel Documentation](https://vercel.com/docs).
-
-[![Deploy with Vercel](https://vercel.com/button)](https://vercel.com/new/git/external?repository-url=https://github.com/vercel/next.js/tree/canary/examples/hello-world&project-name=hello-world&repository-name=hello-world&utm_source=github.com&utm_medium=referral&utm_campaign=deployment)
+[Deploy a Next.js application to Vercel](https://vercel.com/new/git/external?repository-url=https://github.com/vercel/next.js/tree/canary/examples/hello-world&project-name=hello-world&repository-name=hello-world&utm_source=github.com&utm_medium=referral&utm_campaign=deployment) for free to try it out.
 
 ## Self-Hosting