The german autobild car news estimates 50 extra km range (31 miles) with the software update. They don't provide a reference for these claims though....
https://www.autobild.de/artikel/porsche-taycan-2022-test-turbo-s-cross-turismo-preis-reichweite-20911889.html
Software-Update für alle...
Welcome to Taycan ownership in the PNW. I would very strongly advise against finishing the paperwork. You have no idea how long it will take to get this problem fixed. My experience purchasing a Taycan in Seattle was not the most pleasant. At least the drive is a blast.