@Redistro, Thanks for posting in Q&A.
According to your description, I know that you want to know if there is a way to manage apps not listed in the public app and in BYOD phone.
Based on my researching, I found that only protected app can be applied to app protection policy. To manage not listed apps, you can use Intune App Wrapping Tool to wrap a line-of-business app and use app protection policy, or you can utilize the SDK's APIs to customize your app behavior to support features that require your app participation.
Here is more information about Intune SDK and Intune App Wrapping Tool
Hope the above information can help.
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