[Combobox] Implement Combobox

[colmtuite]

Related Issues
Each of these related issues should be considered when designing and implementing the new component. When this issue is resolved, these related issues should be closed.

• [Autocomplete] useAutocomplete hook disabled option can be clicked #44
• [Autocomplete] Refactor useAutocomplete to use Base UI building blocks #45
• [Autocomplete] Fix type for multiple values to use readonly arrays #55
• [Autocomplete][docs] The Tailwind code demo doesn't include item focus styles material-ui#44483
• [Autocomplete] Create the unstyled component #27
• [docs] Document headless Multiple values Autocomplete in Base UI #20
• [Autocomplete] :active pseudo-class styles not applied on option press in Firefox #265

Related issues in Material UI's Autocomplete:

• [Autocomplete] Support values other than raw options material-ui#23708
• [Autocomplete] Differentiate hover & keyboard states material-ui#23916
• [Autocomplete] Update to ARIA 1.2 material-ui#25365
• [Autocomplete] getOptionLabel callback is getting the value instead of option object material-ui#31192
• [Autocomplete] The onHighlightChange event is triggered by child elements of the list item material-ui#31383
• [Autocomplete] ArrowUp must be pressed twice to bypass disabled items above material-ui#32280

[oliviertassinari]

One challenge will be performance https://x.com/diegohaz/status/1848330344941982104.

Also to note that it took me 1,000 hr to get to a point where I started to be happy with the component. 200 hr for the first PR and the rest was iterating with the community on bug reports and feature requests.