I have enabled Modern Authentication on my tenant and it works for Outlook 2016 clients.
I had to apply the following to avoid further basic prompts:
However, for 2013 clients (on Windows 7 Enterprise 64-bit) it doesn't work (meaning it keeps giving basic prompts). They are up-to-date and I have applied the 2 reg keys as stipulated in this article:
I have also verified the minimum versions at:
Is there anything else I can do/check?