Unfortunately the only way you can directly incorporate C# code into SQL is CLR, which would allow you to create a stored procedure that’s compiled from C# code.
Fortunately, while CLR is limited on the libraries / namespaces it supports, you can create a separate web services project as a workaround, and your CLR project can consume those web services, that way you’re not limited on the libraries you can leverage. I used to consume a .NET SOAP web services project in my CLR projects, but you can probably consume RESTful services (such as a modern API) too.
Alternatively, you can use
xp_cmdshell (in a stored procedure) to execute code in the command line on the server. You’d then be able to create a C# application, place it in a folder that’s accessible by your SQL Server instance, and then you can execute a command to run the application, via
xp_cmdshell. But using
xp_cmdshell has more security risks than CLR and is generally not recommended for use.