Hi @Cenk ,
.NET Core is a cross-platform rewrite of .NET Framework. There are many breaking changes between the two frameworks. You can refer to this article to understand the differences between ASP.NET and ASP.NET Core.
Then, when migration, you could refer to the following articles to set the configuration, API controller and so on.
Migrate from ASP.NET to ASP.NET Core
Migrate from ASP.NET Web API to ASP.NET Core.
Besides, since you are using logging, basic authentication, OAuth, and Unity. For this package or class library, you also need to change. In many cases, a replacement NuGet package exists to fill in any gaps left between .NET Framework and .NET Core. In rare cases, you may need to find a third-party solution or implement new custom code to address incompatibilities.
[Note] When using or install the package, you'd better to check the package target framework, make sure it apply to the project version.
Here are some relates articles about logging, authentication, and Identity, you can refer to them:
Logging in .NET Core and ASP.NET Core
Introduction to Identity on ASP.NET Core
Simple authorization in ASP.NET Core
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Best regards,
Dillion