[docs-infra] Migrate to @mui/internal-docs-infra Type Generation

[dav-is]

[!IMPORTANT] This PR is still a work in progress.

Migrates this repo to use @mui/internal-docs-infra loadPrecomputedTypesMeta (being worked on in https://github.com/mui/mui-public/pull/489). Maintains the existing design and theme.

Preview: https://deploy-preview-2932--base-ui.netlify.app/react/components/accordion#api-reference

New Features

• Fixes cache key issue with existing type metadata pipeline
• Removes the need to remember to run pnpm run docs:api, simply running pnpm run docs:build (or pnpm run docs:dev and viewing the page) will update the types
• Supports Hot Reloading Type Meta
• Build time caching for type meta and highlighting per entrypoint
• Using Typescript Language Service API, reduces single page typedoc generation from 4s to 0.3s (93% decrease) with subsequent navigations in 0.15s
• Improved Developer Experience for (Cmd/Ctrl)+Clicking imports in VS Code
• Cleaner diffs for generated files using markdown
• CI checks for Markdown content (e.g. Vale) now run on the typedocs
• Committed files are copied 1:1 into llms.txt markdown version
• Types can be viewed directly in GitHub, which may improve Github Copilot's understanding of the repo

[pkg-pr-new[bot]]

vite-css-base-ui-example

pnpm add https://pkg.pr.new/mui/base-ui/@base-ui-components/react@2932

pnpm add https://pkg.pr.new/mui/base-ui/@base-ui-components/utils@2932

commit: c0e52e3

[mui-bot]

Bundle size report

Bundle	Parsed size	Gzip size
@base-ui-components/react	0B(0.00%)	0B(0.00%)

Details of bundle changes

[netlify[bot]]

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