I am not able to add insigths telemetry to new Asp .NET framework project

There are some other dependencies you need to install as well,

Install-Package Microsoft.ApplicationInsights.DependencyCollector -Version 2.6.4
Install-Package Microsoft.ApplicationInsights.PerfCounterCollector -Version 2.6.4
Install-Package Microsoft.ApplicationInsights.Web -Version 2.6.4
Install-Package Microsoft.ApplicationInsights.WindowsServer -Version 2.6.4
Install-Package Microsoft.ApplicationInsights.WindowsServer.TelemetryChannel -Version 2.6.4

Try as mentioned here

Choose the first option when adding insights, Application Insights SDK. That will install all the necessary packages. Once that's done, you will need to add instrumentation key to the config file. Add that on top.

Your error looks more of source control rather that the project. If you trying to work in source control and adding insights to already checked-in project, may be try creating a dummy project, and add insights to it. That will give more clarity on error, as well as help to pin-point exact issue.