[docs-infra] Add recursively the relative modules in the demos

[mnajdova]

I am testing on the MUI X DataGrid List view example. I copied the example for easier iteration.

TODOs:

• [ ] The docs:typescript:formatted needs to create equvalents for non-component files too, like constants.js, utils.js etc.
• [ ] Support new folders structure when extracting to CodeSandbox/StackBlitz

[mui-bot]

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[mnajdova]

@alexfauquette all comments were resolved in separate commits, you can checke the changes commit per commit. Everything was working as expected (I've tested after all the changes). I noticed one breaking change tough, I described it in the PR description. I am tagging @bharatkashyap too to be aware for it for the Toolpad project. Tagging also @michaldudak I am not sure if this affects the new Base UI docs, but just in case.

[michaldudak]

For the record, the demo loader used in Base UI docs has this functionality built-in already, so once we propagate it to other repos, it should still work fine.