The NumericMenu widget does not have a facet count property. The NumericMenu widget displays a list of numeric filters. Those numeric filters are pre-configured when creating the widget. When a user clicks on a refinement the filter is applied, but the count of records that will match that filter is not known until that filter is applied.
The numericMenu might have 5 price range numeric filters, in order to update the count for each one a separate query would be needed for each item. This would need to happen every time the query changes, each time a user typed a character in the searchBox, 5 queries would be needed to determine the count for each item in the numericMenu.
While this behavior might be achievable with a Custom Widget, it would not be advisable, as each character typed would trigger 6 queries, instead of just one. The reason this is not the case with a widget like the RefinementList is because its items are facet attributes with predefined facet values, the total of which can be calculated by our engine and made available as item.count.
Since the NumericMenu widget has these limitations there's a different approach you can take to get a price range refinement with an item count. The first step is to add an attribute called price_range to all your records. An example record could look something like this.
"price_range": '$10 - $100'
This approach requires the records price range be determined before being added to Algolia, but what this will allow you to do is use a RefinementList and pass "price_range" as the attribute. The refinementList will have the item.count property since the facet values are already available on the records.