refactor: extract base TS client config + upgrade TS + refactor TS setup

[slorber]

Motivation

Move shared client compilation options to tsconfig.base.client.json

(note starting TS5.5 we'll be able to move even more options there, see https://twitter.com/sebastienlorber/status/1781320460732395819)

Rename root tsconfig.json to tsconfig.base.json to make it explicit it's a config meant to be extended.

Upgrade to TS 5.4

Useful preliminary step for #10062

Test Plan

Test links

Deploy preview: https://deploy-preview-_____--docusaurus-2.netlify.app/

Related issues/PRs

[netlify]

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[github-actions]

⚡️ Lighthouse report for the deploy preview of this PR

URL	Performance	Accessibility	Best Practices	SEO	PWA	Report
/	🟠 86	🟢 98	🟢 96	🟢 100	🟠 88	Report
/docs/installation	🟠 59	🟢 96	🟢 100	🟢 100	🟠 88	Report
/docs/category/getting-started	🟠 74	🟢 100	🟢 100	🟢 90	🟠 88	Report
/blog	🟠 69	🟢 100	🟢 100	🟢 90	🟠 88	Report
/blog/preparing-your-site-for-docusaurus-v3	🟠 59	🟢 96	🟢 100	🟢 100	🟠 88	Report
/blog/tags/release	🟠 70	🟢 100	🟢 100	🟠 80	🟠 88	Report
/blog/tags	🟠 76	🟢 100	🟢 100	🟢 90	🟠 88	Report

[github-actions]

Size Change: 0 B

Total Size: 1.59 MB

ℹ️ View Unchanged

Filename	Size
website/.docusaurus/codeTranslations.json	2 B
website/.docusaurus/docusaurus.config.mjs	26.7 kB
website/.docusaurus/globalData.json	91.2 kB
website/.docusaurus/i18n.json	930 B
website/.docusaurus/registry.js	247 kB
website/.docusaurus/routes.js	156 kB
website/.docusaurus/routesChunkNames.json	109 kB
website/.docusaurus/site-metadata.json	2.17 kB
website/build/assets/css/styles.********.css	113 kB
website/build/assets/js/main.********.js	810 kB
website/build/index.html	38 kB

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