If you happen to import the styled API from @mui/styles, then it wouldn't work because it's not provided with a MUI theme out-of-the-box. You need to createTheme and pass it to the ThemeProvider yourself, then augment the type of DefaultTheme because by default it's an empty interface:
import { Theme } from '@mui/material/styles';
declare module '@mui/styles' {
  interface DefaultTheme extends Theme {}
}
But be aware that it's not recommended to use the legacy package @mui/styles. See more detail on my other answer.
In case you've already imported styled from @mui/material/styles: Since you're using typescript, remove the Theme type, the styled function can infer the type of the property theme in the callback, so you don't have to do anything:
const Root = styled('div')(({ theme }) => ({
  background: theme.palette.grey[50],
}))
But theoretically, if the theme is untyped, this is how you add it:
const Root = styled('div')(({ theme }: { theme: Theme }) => ({
  background: theme.palette.grey[50],
}))