docs: add TypeScript playgrounds to docusaurus.new + Playground page

[slorber]

Motivation

It should be easy to try Docusaurus with TypeScript in a code playground

Test Plan

preview

Test links

https://deploy-preview-8723--docusaurus-2.netlify.app/docs/playground

Related issues/PRs

Fix #8685

[netlify]

✅ [V2]

Name	Link
🔨 Latest commit	e6ee135
🔍 Latest deploy log	https://app.netlify.com/sites/docusaurus-2/deploys/6400c698b35edd00082afe0c
😎 Deploy Preview	https://deploy-preview-8723--docusaurus-2.netlify.app
📱 Preview on mobile	Toggle QR Code... Use your smartphone camera to open QR code link.

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[github-actions]

⚡️ Lighthouse report for the deploy preview of this PR

URL	Performance	Accessibility	Best Practices	SEO	PWA	Report
/	🟢 94	🟢 97	🟢 100	🟢 100	🟢 90	Report
/docs/installation	🟠 81	🟢 100	🟢 100	🟢 100	🟢 90	Report

[netlify]

✅ [V2]

Name	Link
🔨 Latest commit	0c1dc75
🔍 Latest deploy log	https://app.netlify.com/sites/docusaurus-2/deploys/6400c7863b860b0008a5d5b9
😎 Deploy Preview	https://deploy-preview-8723--docusaurus-2.netlify.app
📱 Preview on mobile	Toggle QR Code... Use your smartphone camera to open QR code link.

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[github-actions]

Size Change: 0 B

Total Size: 947 kB

ℹ️ View Unchanged

Filename	Size
website/.docusaurus/globalData.json	86 kB
website/build/assets/css/styles.********.css	113 kB
website/build/assets/js/main.********.js	708 kB
website/build/index.html	41 kB

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