The available options update properly when changing the filters so why does the results shortcode not render in this case? I mean, I could put it all on one page and have an empty result template make the shortcode render but then I would lose the link to the external results page (that has all the url parameters set up properly).
Is there a workaround, with an empty template. But how could I create the link to the results page with all the url filter parameters?
Unfortunately there isn't a workaround for this. The [wpv-found-count] shortcode requires that the results be on the same page.
If the results are not there then the [wpv-found-count] shortcode has no way of telling how many items are being displayed.
Not much we can do about this since this is how it works by design.
The results section generates a separate div that the [wpv-found-count] will detect and gather the number of items found. When the Filter is separated from the view, essentially this div is not present on the page.