@Angela Calborean , Thank you for posting this question.
I understand that you are trying to follow the steps mentioned in the following article to configure Application Insights for your ASP.NET Core web API project- Application Insights for ASP.NET Core applications
I see that the package mentioned in this article, Microsoft.ApplicationInsights.AspNetCore, depends on Microsoft.AspNetCore.Http which is deprecated.
I am reaching out to our AppInsights team for clarification regarding it and will update this thread soon.
Regarding your question, if you are only interested in capturing custom logs (for example using ILogger.LogInformation/warning
etc.), you can follow the steps mentioned here - Application Insights logging with .NET. Note that it will only enable logging and no other telemetry (request, dependency, exceptions etc.).
Another option would use Open Telemetry based instrumentation which is in preview, which has its own set of opentelemetry based packages and supports most of the scenarios covered in default package. For more details, see Enable Azure Monitor OpenTelemetry for .NET applications
Hope this helps. I will update this thread regarding the package mentioned in question which depends on a deprecated package.