This is still under review by the feature team.
An error occurred while saving the commentPaul Hendrick commented
I came here to say that the system's native emoji picker should be supported - for example on macOS you can open it this in any textfield with with "⌘ ^ Space" - but this doesn't work in Teams.
You can paste emoji into teams if you enter them in another app and copy them out - so it's not like the unicode support isn't there...
Now that I've discovered the EmojiOne support (thanks, Nathan Smith!), I'm a little happier. I actually use this as my system emoji font anyway.