Dear Gylfi Már Ágústsson
Good day! Thank you for posting to Microsoft Community. We are happy to help you!
Based on your description, To turn on auto capitalization of the first word of a sentence in the New Outlook, please follow these steps: click create a new message>click Message>click options like following>choose change case>To capitalize the first letter of a sentence and leave all other letters as lowercase, click Sentence case. For your reference

If you still need further help or I misunderstood your meaning, please kindly correct me and tell me more details so that I can do further research and tests, thanks.
Thanks in advance for your understanding! Your patience and cooperation will be highly appreciated. Hope you all the best!
Sincerely,
Kerry Chen | Microsoft Community Moderator