OP here. I launched Thursday on PH yesterday (Thursday) and shared our metrics publicly. These include unique visitors (by the time of the day), browser, OS, and countries. I also added conversion data.

Thursday is a simple web app with no sign-up, so our conversion metrics will differ from most other products. So yes, your mileage will vary. But I believe the traffic could be a good indicator of what to expect from a PH launch. Now, that too might vary by the day of the week.

I'm getting the traffic data from Amplitude, and the conversion-related data from our database.