Using Classic Outlook on Windows for personal email, calendar, and contact management
i can explain. If you read my posts you will notice I already said that hotmail has the dns records already setup. Your lookup confirms that is correct. You are having a problem getting it to work apparently, and in that case do you have a premium account? If so login to your hotmail account and go to the defender portal and setup the policy.
According to public documents I posted for you, the free accounts to not support dkim signing for live, outlook, or hotmail addresses, even through DNS records exist. If you think that documentation is wrong you can use the feedback link at the bottom of the page to suggest an update. You should reach out to support because people here will not want to help if you are abusive to the community.
Good luck