chore(examples): Convert api-routes example to TypeScript

[maxproske]

Converted API Routes example over to TypeScript to match the Contribution guidelines.

Documentation / Examples

• Make sure the linting passes by running pnpm lint
• The examples guidelines are followed from our contributing doc

[balazsorban44]

Let's consider #38091 (comment) on this and all future PRs!

[maxproske]

Thanks @balazsorban44 - I made your requested change.

I thought function over const only applied to pages, but I'll consider components going forward.

[maxproske]

@balazsorban44 Thanks! Made your requested change, and ready for re-review!

Can I also get confirmation that you recommend export default function over split const/export for components, in addition to pages and API routes in examples?

[balazsorban44]

Thanks!

As for #38083 (comment), I think, for consistency's sake, we should use function over const/let uniformly, yes. default exports might not be necessary though (unless a page or API route), because a file could export multiple things, but these are stylistic details and a grey area what we should enforce vs. prefer.

So (in my opinion) use function whenever possible, but at the minimum for API Routes and pages. Rest should be at least consistent throughout the example. 👍

[balazsorban44]

Opened #38511 to discuss the above and add it to the contributing guidelines