[InputBase][material-next] Add InputBase component

[mj12albert]

Part of #38374

Migration Steps

• Copy component files from material (v5) to material-next (38392)
• Remove deprecated components and componentsProps props (38392)
• Drop support for ThemeProvider in favor of CssVarsProvider (38392)
• Migrate component to Typescript (38392)
• Refactor component to use Base UI’s hook if it exists (38392)
• Implement Material You design specs InputBase contains mostly reset styles
• Add component playground to v5 docs will be part of the TextField playground
• Refactor styles to use component CSS Variables (38392 but will be polished when working on TextField)

Other tasks

• Port/relocate tests to useInput.test ([Input][base-ui] Update and port additional tests from material-ui #39584)
• Integrate with material-next/FormControl ([FormControl][material-next] Add FormControl component #39032)
• Add sx type ([InputBase][material-next] InputBase slotProps accepts sx type #39714)