ProtonMail App doesn’t have offline mode enabled by default. It’s funny, you can see the list of emails but can’t read any of them.
Here is how to enable the offline mode:
Go to Settings -> Account Settings -> Privacy -> Auto-download messages
Note, that this will only download emails when there is a sync notification such as this one:
I have no idea how often does this happen though. Let’s be patient?!
After a while, I’m able to view emails offline:
Seems like background sync must be enabled too: https://protonmail.com/support/knowledge-base/not-receiving-push-notifications/
Offline option customer request: https://protonmail.uservoice.com/forums/284483-feedback/suggestions/11261736-create-an-offline-option