Hi @Tom Lee,
According to my research, there are other on-prem Exchange users who have reported this phenomenon, and the following official documentation of the Outlook client on the mobile side mentions that the synchronization of draft folders is only applicable to “specific account types”, while email accounts hosted on Exchange 2016 is not explicitly mentioned as a supported account type. Please see Does your app support draft syncing? So taken in the round, personally I assume for Exchange 2016, it may be not supported at present.
Then please understand that actually the “outlook management” tag is for issues related to Outlook for Windows and Outlook for Mac. Since your query is about Outlook for mobile, I am afraid hardly we can help on this. In case you would like to confirm further or need more assistance, I’d recommend trying to contact the in-app support, see Get in-app help for Outlook for iOS and Android. Or you can visit the dedicated Outlook for Mobile forum below for help:
Outlook for Android: https://answers.microsoft.com/en-us/msoffice/forum/msoffice_outlook-mso_amobile
Outlook for IOS: https://answers.microsoft.com/en-us/msoffice/forum/msoffice_outlook-mso_imobile
If the answer is helpful, please click "Accept Answer" and kindly upvote it. If you have extra questions about this answer, please click "Comment".
Note: Please follow the steps in our documentation to enable e-mail notifications if you want to receive the related email notification for this thread.