According to your error message, I suppose your issue is about when you try to deploy to a machine that does not have the CLR Types for SQL Server installed.
You said you have installed the Nuget package, so I suggest you could also check whether the appropriate version of the native SqlServerSpatial110.dll assembly is copied to the output directory and deployed with your application. For more details about this issue, you could refer to this article.
You could also check whether you have installed the Microsoft System CLR Types. Fore more details ,you could read this SO thread.
After a lot of research I just installed "Microsoft System CLR Types for SQL Server 2012" from:
X86 - http://go.microsoft.com/fwlink/?LinkID=239643&clcid=0x409
X64 - http://go.microsoft.com/fwlink/?LinkID=239644&clcid=0x409
Worked like a charm!
Besides, If I use SqlGeography in Microsoft.SqlServer.Types package, it works fine on my side:
The code in Azure function:
The result in Azure portal: