Opening the emoji tool is pretty snappy. However, switching between pages can take up to 5 seconds before options are rendered. Since there is no page picker, scrolling to the 3rd or 4th page can feel tedious.
I suspect this might be because adding an item to the bar is somewhat expensive, and especially so for large pages with many items. Maybe the list can be rendered in a virtualized way.
I think that the native iMessages emoji picker sets a good model for how the widget should behave.
Even if it were just one long scrolling list with no fast category switching, that would be fine. That's basically what apple's is anyway, and it works.