[core] Use re exported utils from packages in docs examples

[LukasTy]

This is a follow-up to: #13823 (comment)

• Add <package>/utils export with utilities, that are used within documentation examples
  • Add paid package re-exporting of such utility from base package (Charts, Pickers)
  • What to do with DataGrid? It already has utils export and it is also re-exported on root. 🙈
• Use new re-exports in the documentation examples in turn "hiding" the @mui/utils usage from end users

[mui-bot]

Deploy preview: https://deploy-preview-13901--material-ui-x.netlify.app/

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[github-actions]

This pull request has conflicts, please resolve those before we can evaluate the pull request.

[flaviendelangle]

This PR is several month old, is not a draft but has no review requested
What is its current state?

[mnajdova]

The general direction of the PR makes sense to me, but I wouldn't want to be the reviewer, as I am not fully aware of the scope and usage of these utils in all X products :)

[flaviendelangle]

The logic seems nice to me
I just wonder what it should look like once we have Base UI X (and stuff like useId is in the Base UI utils package)

Do we export from Base UI X packages AND MUI X packages ?
Do we only export from the Base UI X packages ?
If the Base UI utils package is public, do we say to people to use it directly ?

Just to avoid doing something we would undo in a few months