The selection of points only works while you are in direct_select mode. The easiest way to tell if you are in that mode is that the midpoints of the edges of your polygon is visible.
The editing mode is now displayed on the map, for better UI clarity. However, since mapbox-gl-draw is buggy, it will not always report the correct mode.
There is also an existing bug that whenever a feature is edited, this triggers an update to the props.features externally, but then this triggers an effect which deletes and recreates all the features in mapbox. The net result is that any feature you edit is immediately deleted and replaced by a duplicate any time you let go of the mouse.
I was unable to fix a bug where if you upload the GeoJSON and then cancel the edit, the map will still show the changes that were cancelled, until you go back in to edit mode.