[pickers] Sustainable public API for customization

[LukasTy]

Created from https://mui-org.slack.com/archives/C04U3R2V9UK/p1702930558019959

Might be missing MuiDayCalendar-header or it's not clear in documentation for style override

This feedback sparked a higher-level discussion regarding our strategy for public API.

Problem

Picker components are composed of many smaller components, which might have very relevant information regarding Pickers' styling options. Like in the linked feedback, a user noted that we do not document the relevant classes for styling the internal parts of DateCalendar.

Solution

The default approach that we most often take in such cases is to make a component in question public. Such an approach could pose a huge threat down the road because we will eventually have almost every component public and almost no room to make changes without introducing BCs.

Alternative solutions

• Consider having the option to document internal component API and/or CSS class documentation.
• Expose dayCalendar classes from DateCalendar.

Any other proposed solution, which would bring more clarity to the users, without digging an even deeper grave. 💀🙈

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