I renamed set_count_internal to update_count_in_dom, because "internal"
was redundant in terms of saying the function was private, and it misled
me into thinking it was internal-only in impact, but it actually updates
the DOM.
I also removed the synchronous callback functions, since they both
led to simply hiding the count_span and clearing the text of the
value_span.
(imported from commit dea27d6414dc1b33818b24662f8246d687530b71)