Is there a way to add claims in an ASP.NET Core middleware after Authentication?

Yes it’s possible, but instead of adding to the list of existing claims you have to add a new identity of type ClaimsIdentity.

public class SomeMiddleware
{
    private readonly RequestDelegate _next;

    public SomeMiddleware(RequestDelegate next)
    {
        _next = next;
    }

    public async Task InvokeAsync(HttpContext httpContext)
    {
        if (httpContext.User != null && httpContext.User.Identity.IsAuthenticated)
        {
            var claims = new List<Claim>
            {
                new Claim("SomeClaim", "SomeValue")
            };

            var appIdentity = new ClaimsIdentity(claims);
            httpContext.User.AddIdentity(appIdentity);                
        }

        await _next(httpContext);
    }
}