Add code examples to the home page

[IanButterworth]

Fixes #2289

Just some starter code ideas from me and Claude.

https://julialang.netlify.app/previews/pr2406/

[github-actions]

Once the build has completed, you can preview your PR at this URL: https://julialang.netlify.app/previews/PR2406/ in ~15 minutes

[DilumAluthge]

Nice!

[ViralBShah]

Nice!

In the very first Nutshell example, the end is a bit misaligned. Can it be lined up? This formatting seems to be an issue in all the examples.

@StefanKarpinski

[DilumAluthge]

Ah, I agree, it would be nice to fix the alignment on the dangling end.

Once that's fixed, I say let's give this a shot? Seems like an improvement over the status quo.

[IanButterworth]

Fixed the indenting and I checked that all of the examples run.

Yeah, maybe it's ok to merge this sooner and crowdsource improvements to the examples.

[ViralBShah]

Works well on mobile

[ViralBShah]

Oh damn I see there was a recent commit in flight. I suppose simplest to have new PRs.

[ViralBShah]

Now to see if one of those examples can be a JuliaC one.