Assuming that you have the old email address and password, email magix at infoservice@magix.net and ask them to merge the old account with the new account you have created here - you may have to wait until early next week for this to be done as we are now entering the weekend.
The version of Video Easy you have is very old, no longer supported and, having a P2- serial number, it may not be possible to activate it.
If you do manage to get it activated you will need the latest drivers for the USB capture device from here, and in Windows 11 Settings, Privacy & Security, Camera and Microphone options turn on the Let desktop apps access your camera/microphone options - you may need to scroll down the relevant page to see this option
All products since 2014 have serial numbers beginning with P3- which using a different activation process to the P2- and earlier serial number formats.