@brichardi Thanks for posting in our Q&A.
If requiring Outlook apps to prompt for password when launch, only an app protection policy will meet the requirement. One of the options in the app protection policy is Require PIN for access, this would prompt a user to enter a pin when accessing the Outlook that is managed.
https://learn.microsoft.com/en-us/mem/intune/apps/app-protection-policy-settings-android#access-requirements
In the following page, we can configure the access requirements what we need.
Hope it will help.
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