I encountered a similar problem recently. In a solution file, I have my library project and a web API project. In both projects, I installed a nuget package of a different project I own. I had a problem of locally referencing that project in the web API.

This was because I had referenced the nuget package in the library, I couldn't use a local reference in the web API. This is not mentioned in any of the error messages. I knew it was a problem only on the web API because the assembly path updates when I add the reference to other projects.

So it should also help if you look into your references if any are causing conflicts with your library DLL. It might be that other referenced libraries/projects you have in the new web app is using a different version of the library DLL.