If that’s the case then I believe just controlling notifications for those two apps for each focus probably gets you what you want. Then also go to iOS Settings > Outlook > and disable the authorization for it to use Time Sensitive Notifications. I have a similar setup on my devices.
Funny you say that, setting it up without internet is one of the few ways left to still be able to create a local account.
That’s the point of “time sensitive”, That it bypasses focus. Perhaps you can disallow the time sensitive option in settings and just allow all notifications from that app in the other focus modes that you want and disallow in the ones you don’t?
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US based apps that’s are end-to-end encrypted where you control the private keys cannot physically share as they won’t have access. Even if it’s in their cloud.