This is a common problem with any app that includes the new System Extensions. If you do not uninstall it properly, then it gets baked into the operating system at a very low level. Unfortunately, many 3rd party uninstallers don't work and leave this file installed and running. Sometimes people use 4th party "app zappers" or "clean up" tools that can't possibly work. The only guaranteed way to remove a System Extension is to drag its containing app to the trash. As you might expect, people who ship apps that contain System Extensions tend to store their containing apps in hidden folders. 😄
There is a way to remove these System Extensions, but it is difficult and dangerous. It involves using the Terminal, Recovery mode, and disabling system security. The easy way is to erase the hard drive and reinstall the operating system.
If your case, the fact that you're getting a new computer is pretty much the same thing as having erased the hard drive and reinstalled the operating system. What you can do is be careful when you restore from backup. Do NOT restore any apps, software, system settings, or "other files". You can restore your user files and user accounts only. Then, manually reinstall any 3rd party apps that you really need. If any of those apps need administrator privileges or special "approvals" to install, consider that very carefully.