As I understand it, the Emoji keyboard is based on text substitutions.

Text prediction, emoji access and video controls are a pleasure to use in Safari, among other Touch Bar things elsewhere in macOS. I miss them in Chrome. At first glance they may seem simple and unnecessary, but when in use they feel intuitive and with time become quite significant UX additions.

Issue 42434 hasn't been updated since May, so I hope some attention can come out of this to look into these requests.

Text prediction is being worked on right now. Once that's completed, we'll move on to emoji keyboard. Keep in mind, working with text in the web contents is difficult, so it will take some time.

Any news on this? Emoji support in the Touch Bar would be really great. 

Not currently scheduled.

Well, now with the typing suggestions from 717553 it suggests emojis too. I think there is a flag, it's still not in stable. 
It'd be great to have alongside the text predictions and emoji button which would reveal the emoji picker !