AssemblyInfo patching happens only once during build job. That's why I would recommend to implement build matrix to split build to 2 separate jobs. You can create 2 configurations in VS, and tune them so each configuration builds only specific part of the projects. Set those 2 configurations in YAML or on Build tab (if you use UI).
Then then you can specialize settings for AssemblyInfo patching for different matrix jobs.
Build will contain 2 jobs, but it should not take significantly more time as each job will build only part of projects. And if you have spare concurrent job, it will be actually faster.
Another advantage of this is clear separation of artifacts, especially indeed they are different products.