[material-next][Search] Add new `Search` component

This issue is to track the work for adding the new Search component to @mui/material-next, moving forward the Material You effort (https://github.com/mui/material-ui/issues/29345)

Material You Search specification: https://m3.material.io/components/search/overview

Ideas:

• Create one component with a variant prop, which can be 'searchbar' or 'searchview'
• Create two components:
  • SearchBar, which is rendering SearchView on focus
  • SearchView

I think the second option is the better one, as this way the SearchView can also be used without the SearchBar and the logic of the SearchBar is not implemented unnecessarily.
However, I would like to collect further suggestions or approvals and then start with the implementation.
If my suggestion is accepted, I would first implement the SearchView and then the SearchBar.

Note: This comment will be updated to show the progress, ideas and list possible issues.

@DiegoAndai