[internal] Fix regression broken ad on Joy

[oliviertassinari]

A better fix for #35685 following #35096 (comment). A solution that flattens the context: it implements https://www.notion.so/mui-org/Site-styling-architecture-e781897a38904671ba909c51dcb28f83#d7235018176745e2b067f5570e6e0197. We never get more than 2 theme providers nested:

• _app: no more theme context: keep the playground pristine
• first page: add the MUI brand context
• demo: add the Material UI or Joy UI default theme.

[mui-bot]

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[mnajdova]

Seems like we can now merge these two components into one, to ease up the implementation. They are used together everywhere.

[siriwatknp]

@oliviertassinari Let's do the quick fix in this PR (so that we can merge it) and I will open another one for removing the global ThemeProvider (it will take some time but I think it is the right way to go)

[oliviertassinari]

@siriwatknp Ok, the regression first: #35685.

I will open another one for removing the global ThemeProvider (it will take some time but I think it is the right way to go)

👍 The PR wasn't too far from making it work, but I abandoned it. Looking at the commits, I spent 1 hour on a Sunday's night, made it work locally pushed, and went to bed, unfortunately, the CI didn't pass 😅.

[oliviertassinari]

We still need to flatten the theme providers, the whole docs structure feels completely broken right now.

I'm not aware we have a GitHub issue that tracks this, so I'm reopening to have something open that reflects this problem. Happy to have this moved to a GitHub issue though.

[siriwatknp]

I am closing this one in favor of #45386