Why did HR want me to do online training for a job I am no longer going to have on my last day of work? How dense and clueless is she?

She may be covering herself. It's possible it was her responsibility to see that you received the training at some time during your employment. Now that you're leaving, it has come to her attention. At this point, you taking the training is designed to facilitate her agenda, not yours.

She may be covering herself. It's possible it was her responsibility to see that you received the training at some time during your employment. Now that you're leaving, it has come to her attention. At this point, you taking the training is designed to facilitate her agenda, not yours.