In my experience, people will generally have their build server be the source of truth for the build number/versioning. This also allows you to pass around the version number to different systems and/or notifications, etc more readily.
You may want to look into having your build server handle the versioning for you. For Azure DevOps you can do this under you pipeline Options > Build number format (or something like that). I think this bit of documentation might help: Run (build) number - Azure Pipelines | Microsoft Docs.
With your current process you would need to read the value from the Assembly Info and then set a variable to that value which you could then pass into the steps which need it. It looks like there might be some existing extensions which would allow this such as: Assembly Info Reader - Visual Studio Marketplace which would expose a variable you can use
I hope this helps!