Also it would fallback to a text input in unsupporting browsers which is quite different to what is desired imo.
Tbh I think a window.showEmojiPicker() is probably a good first step anyway. Give people a JS way to invoke it and use the selected character somehow?
We often want to insert the chosen emoji into a textarea or something, so the picker itself being an input feels wrong regardless. <button emojipicker> is perhaps a better design for progressive enhancement?
Perhaps we add a showEmojiPicker to input, textarea and contenteditables and then add a new button command that triggers this? Idk sure my ideas have flaws but all this is to say a new input type is not the answer imo.