[discussion] Add Emoji Picker component?

*⚠️ Info: This issue is for product research, to gather community input. In this [base-ui repo](https://github.com/mui/base-ui) we are, currently, focused on the core set of components needed to create a great design system, so the probability we build this in this repo is very low.*

## Summary

## Examples in other libraries

- https://github.com/liveblocks/frimousse
- https://github.com/missive/emoji-mart

*([internal benchmark](https://www.notion.so/mui-org/x-Emoji-Picker-35ccbfe7b66080f4b345d443754eea52))*

## Motivation

TBD

- User requests:
- /
- UI library requests:
- https://github.com/mui/mui-x/issues/3759