Now Google brings support for symbols and special characters in the emoji picker in ChromeOS. This feature is available in the latest stable version of ChromeOS.
In the recent version, you can see the emoji picker has to enlarge new special character included including Arrows, Bullets/stars, Currency, Letterlike symbols, Mathelike symbols, and Miscellaneous symbols.
Earlier ChromeOS only supported the typing of special characters with a keyboard shortcut and a set of numbers. How it works Andrew Romero explained last year, although, in the short version, you need to use Ctrl + U for using special symbols.
Most of the time users prefer visual pickers which are easy to use and like Windows. For using this emoji picker special character you need to right-click or Search+ Shift keyboard shortcut.
Finally, in this emoji picker, a new section also appeared, used for text-based and called emoticons.