After a few more hours of digging, I think I was finally able to resolve the issue and now when I'm accessing / I get status 200. Respectively this can be changed to any path. Here is the code that I made it working with:

app.Use(async (context, next) =>
{
    if (context.Request.Path == "/")
    {
        context.Response.StatusCode = 200;

        return;
    }

    await next();

});