[autocomplete][material-next] Add Autocomplete component

Part of https://github.com/mui/material-ui/issues/29345, related to https://github.com/mui/base-ui/issues/45

This is an umbrella issue to refine the scope and track work for the v6 Autocomplete

Scope (not yet finalized)

Keep in mind we want to minimize breaking changes

• Convert to TS (also part of https://github.com/mui/base-ui/issues/45)
• Implement slots and slotProps (only slotProps is currently supported) as a replacement for renderInput, though it may be a good idea to not drop it immediately
• Fix https://github.com/mui/material-ui/issues/29381

Breaking changes (accepted in the past, but unmerged/on hold)

• https://github.com/mui/material-ui/pull/36389
• https://github.com/mui/material-ui/pull/37301

Dependencies

• Popper https://github.com/mui/material-ui/issues/39965
• ListSubheader
• Paper https://github.com/mui/material-ui/issues/39964
• IconButton https://github.com/mui/material-ui/issues/39943
• Chip https://github.com/mui/material-ui/issues/38024
• InputBase https://github.com/mui/material-ui/issues/38372
• OutlinedInput (only the classes) https://github.com/mui/material-ui/issues/39695
• FilledInput (only the classes) https://github.com/mui/material-ui/issues/39052

All current Autocomplete issues: https://github.com/mui/material-ui/issues?q=is%3Aopen+is%3Aissue+label%3A%22component%3A+autocomplete%22+-label%3A%22package%3A+joy-ui%22

Start with this umbrella issue and its linked base-ui, Popper, Paper, IconButton, and OutlinedInput issues; the scope is explicitly not finalized. Confirm the v6 requirements and dependency status before estimating implementation, with completion defined by an agreed scope and tracked Autocomplete work.