How to return html page from WebApi action?

One way to do this is to read the page as a string and then send it in a response of content type "text/html".

Add namespace IO:

using System.IO;

In the controller:

[HttpGet]
[ActionName("Index")]
public HttpResponseMessage Index()
{
    var path = "your path to index.html";
    var response = new HttpResponseMessage();
    response.Content =  new StringContent(File.ReadAllText(path));
    response.Content.Headers.ContentType = new MediaTypeHeaderValue("text/html");
    return response;
}

For ASP.NET Core (not ASP.NET Standard) then if it's a static html file (which it looks like), use the static resource options:

Static files in ASP.NET Core