[code-infra] Cleanup @mui/docs usage and legacy re-exports

[LukasTy]

• Make mode undefined in BrandingProvider as this case is handled in the component
• Remove no longer used @mui/docs re-exports from docs/src/*
  • [code-infra] Cleanup monorepo and @mui/docs usage mui-x#13713 and [code-infra] Use @mui/docs where possible toolpad#3751 ditches last remaining usages
  • Update imports of usages in the codebase to rely on direct imports from @mui/docs
• Use MarkdownElement from @mui/docs instead of the re-export

[mui-bot]

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https://deploy-preview-42833--material-ui.netlify.app/

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[LukasTy]

@Janpot I've also removed HighlightedCode, Link, and MarkdownElement re-exports due to the changes in toolpad: mui/toolpad#3751.
Requesting a re-review.
P.S. I've tried moving the HighlightedCode.test.js file to mui-docs package, but that introduced TS issues.
Do you think it's worth setting up testing on mui-docs or can that be left for a separate effort?

[Janpot]

I've think I've ported some of the tests last time. aren't they running? i may have not verified this week enough

[LukasTy]

I've think I've ported some of the tests last time. aren't they running? i may have not verified this week enough

Well, there are no test dependencies in this package: https://github.com/mui/material-ui/blob/next/packages/mui-docs/package.json 🙈 🤔

[Janpot]

Ah, it was in an upcoming PR

[LukasTy]

Ah, it was in an upcoming PR

Sorry, I didn't see it. 🙈