There is an existing feature request here, that you may wish to support:
For now, I will keep your feature request open as a separate request, with the understanding that you are asking specifically for a setting analogous to the current Settings > Appearance > Extension Width, but for height — thus, as specified in your topic title, the proposal is that there should be an additional setting Settings > Appearance > Extension Height, with the options “Default”, “Tall”, and “Extra Tall”.
In contrast, the existing feature request is more general, and may encompass solutions such as a draggable window border for resizing to arbitrary dimensions.