[material-ui][joy-ui] Add InitColorSchemeScript for Next.js App Router

[siriwatknp]

Cherry picked from #42247 to unblock MUI X on mui/mui-x#13712

• I have followed (at least) the PR section of the contributing guide.

[mui-bot]

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• docs/data/joy/customization/dark-mode/dark-mode.md
• docs/data/joy/main-features/dark-mode-optimization/dark-mode-optimization.md
• docs/data/material/experimental-api/css-theme-variables/customization.md
• docs/data/material/experimental-api/css-theme-variables/migration.md
• docs/data/material/experimental-api/css-theme-variables/usage/usage.md

@material-ui/core: parsed: +0.11% , gzip: +0.14%
@mui/joy: parsed: +0.12% , gzip: +0.16%

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[mnajdova]

Suggested change

	To [prevent the UI from flickering](/joy-ui/main-features/dark-mode-optimization/#the-problem-flickering-on-first-load), apply `<InitColorSchemeScript />` before the main application script－it varies across frameworks:
	To [prevent the UI from flickering](/joy-ui/main-features/dark-mode-optimization/#the-problem-flickering-on-first-load), add the `<InitColorSchemeScript />` component before the `<CssVarsProvider />` component:

Maybe rephrase, as it is no longer a script.

[mnajdova]

I've added one comment on the instructions. As it is cherry-pick I am not diving too deep into the implementaiton.

[cherniavskii]

Thanks @siriwatknp
I've added a comment about this in #42247 (comment) before I discovered this PR 👍🏻

To double-check, is the deprecation notice intentional for the v5?
Since the getInitColorSchemeScript is still available in v6 (and deprecated), perhaps v5 shouldn't log deprecation messages that could e.g. make the tests fail?

[siriwatknp]

To double-check, is the deprecation notice intentional for the v5?
Since the getInitColorSchemeScript is still available in v6 (and deprecated), perhaps v5 shouldn't log deprecation messages that could e.g. make the tests fail?

Yes, the deprecation should happen on v6. I will open another PR to remove the warning.