I had acquired Vegas Movie Studio 16 Platinum as part of an Intel promotion on purchase of a new laptop. The software package included MAGIX Music Maker and PC Tune In. It also included VEGAS DVD architect. All of these have been successfully downloaded and installed on my machine. I have managed to use each item with no problem except that of the DVD architect 7 (Version 2020.006.20042) which requires me to enter a serial number and I didn't get one for it, despite it being downloaded as one along with the others.
Vegas has its own forum. See the Important Message at the head of this forum for redirection details.
Your seller should have provided the serial number. Try going to the Magix account https://www.magix.com/us/support/my-service-center/ you had to create and look under My Products. You may find the number there.