We do not have any sort of counter for this anywhere on the network, not on a per-site or network wide basis... though that's not because it's not potentially interesting information. We didn't track whether a question was on the HNQ list until February 2019, so creating a feature like this wasn't possible until then.
That said, if we ever did create it, it'd be very incomplete as we can't create the data looking backwards before February. We just don't have the information. So, any tool would come with the giant asterisk "Data since February 2019".
If you are interested in the partial data you can probably do this in SEDE by requesting the count/site for the appropriate history event - I'm a bit sketchy on how such a query would work but there are some users here on MSE who are great with SEDE and may be able to help you with it.