This issue is to track the work for adding the ButtonGroup component to @mui/material-next, moving forward the Material You effort (#29345)

Material You SegmentedButton (this styles should be used for ButtonGroup) specification: https://m3.material.io/components/segmented-buttons/overview

Migration Guide steps

• Copy component files from material (v5) to material-next: [material-next][ButtonGroup] Copy ButtonGroup to material next #39739
• Remove deprecated components and componentsProps props: Skipped, no props to remove
• Drop support for ThemeProvider in favor of CssVarsProvider: [material-next][ButtonGroup] Apply MD3 style to ButtonGroup #40124
• Migrate component to Typescript: [material-next][ButtonGroup] Change ButtonGroup files to ts #39794
• Refactor component to use Base UI’s hook if it exists: Skipped, no hooks needed
• Implement Material You design specs: [material-next][ButtonGroup] Apply MD3 style to ButtonGroup #40124
• Add component playground to v5 docs: [material-next][ButtonGroup] Apply MD3 style to ButtonGroup #40124

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

@DiegoAndai