feat(docs): add the input playground at /playground/input

[myromartsin]

Summary

Add an interactive playground at /playground/input. Every setup renders the live field, the controller state, and the code that reproduces it, shareable through URL parameters.

Motivation

A runnable field demonstrates the controller faster than prose.

Conformance impact

None.

Checklist

• Tests added or updated (or a rationale for why none)
• pnpm test, pnpm lint, pnpm format pass locally
• Docs reflect the change (per CONTRIBUTING.md)
• Commit message follows the project convention

[github-actions]

Site preview: https://3d6f3066.telixon-landing.pages.dev

[codspeed-hq]

Merging this PR will not alter performance

✅ 39 untouched benchmarks

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_{Comparing feat/playground-input (4e72579) with main (b37d0a6)}