The App for Outlook attempts to show the last/next activity for each email recipient. It will only do this if the activity is set as regarding that specific contact. This is flawed because an activity is rarely regarding a single contact. It will either involve multiple contacts or be regarding a campaign, opportunity etc.
A few examples where this does not work:
1. Appointment with 3 contacts (regarding an opportunity). Does not show for any contacts in the Outlook app.
2. Appointment with a single contact (regarding a campaign). Does not show for contact in the Outlook app.
3. Appointment with 3 contacts. Can show for only 1 of the 3 contacts in the Outlook app, if that contact is the regarding lookup.
There are views in the browser application that are capable of showing all related activities, not just those where regarding is set as the contact. Without this in the Outlook app, the next/last activity cards may as well be removed.
I raised this as an idea last year (https://experience.dynamics.com/ideas/idea/?ideaid=6894c87e-e1e1-e811-b96f-0003ff68a2c7) but did not get any response or feedback. It is surprising that no one else seems to think this is an issue.