You are awesome! Absolutely correct, ping the line does not take into account the bow offset. That’s a failure of documentation. To ping the ends of the line you should align the mark as close to the phone’s GPS location as possible.
I decided not to use bow offset for pinging the line (or the marks) as I couldn’t be sure from which direction you would be approaching the line end, sometimes you’ll run the line, sometimes approach the end from downwind, so I took the approach to use no offset. This is also true for pinging parks of the course.
But the bow offset IS used for the Distance to Line (DTL) and assumes you’re approaching the line at 45 degrees, using the cosine rule you noted.