Convert active-class-name example to TypeScript

[maxproske]

The Contributing guidelines say TypeScript should be leveraged for new examples, so I thought I'd convert this example over.

I also:

• Upgraded all dependencies
• Replaced the prop-types package with TypeScript types

Documentation / Examples

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

[maxproske]

A couple questions before I continue converting examples to TypeScript:

• Should TypeScript examples be named with-whatever, and examples that call for a separate JavaScript example be named with-whatever-javascript going forward?
• Should TypeScript strict mode be enabled? I see 11 examples have it enabled, and 16 have it disabled (including the with-typescript example itself).

[balazsorban44]

Thanks! 💚

[balazsorban44]

Regarding #37676 (comment)

• I don't think we need a distinct name for JavaScript/TypeScript folders. "examples that call for a separate JavaScript example" Which one is this?
• I think the default tsconfig.json created by Next.js disables it, so I would go with that.