Issue for adding FormControl to @mui/material-next as part of the Material You effort (#29345)

Open questions/discussion

• What is the recommended/correct way to "extend" Base UI's FormControl?
• Decide how to extend Base UI FormControl's onChange [FormControl] Integrate FormControl with input components base-ui#17

Migration Guide checklist

• Copy component files from material (v5) to material-next, including tests, types, and utils PR
• Migrate component to Typescript PR
• Remove deprecated components and componentsProps props, leaving only slots and slotProps PR
• Drop support for ThemeProvider in favor of CssVarsProvider FormControl doesn't consume any tokens
• [ ] Refactor component to use Base UI this is more of a new feature
• Implement Material You design specs - it only contains reset styles and doesn't use any tokens
• Add component playground to v5 docs will be done at the TextField and Select level
• Refactor styles to use component CSS Variables - it only contains reset styles and doesn't use any tokens

Tasks

• Migrate the 'should not warn when toggling between inputs' test from InputBase, it was dropped in 38392 - [FormControl][material-next] Add FormControl component #39032
• Add the sizeSmall class - [FilledInput][material-next] Add FilledInput component #39307 (comment)