A quick update for this in case it helps anyone / saves them from applying the faulty patch and making matters worse!
With this issue I click the map, which should place a point, generate a buffer, and intersect (I have moved away from the features I would intersect so as to not show this data, but the same occurs next to features also):
When I click it says "Clear Search Location" at the top, though no search is performed.
After further testing the issue was found to be in relation to the fact that I had removed the Esri World Geocoder from the search options. Without the Esri World GeoCoder the Nearby App was not able to perform buffer / intersect function. It was able to place a point to perform text searches, but would not generate a coordinate/buffer from a map click.
When the default Esri World Geolocator is added, click/buffer/intersect works again:
Esri have indicated that they will update the documentation for the Nearby App to indicate that an Esri World Geocoder is required.
I had also attempted to use the W3W locator in place of the Esri World Geocoder, but this did not work.
Hope this helps,
Dean