I'm using both the desktop and web versions of Outlook with D365 Sales and am provisioned/licensed correctly with the D365 App for Outlook. Sync is configured properly with server-side Exchange of mail, appointments, contacts, etc.
I could swear there used to be a way to pick a contact from your contact list in Outlook and manually choose to track it in Dynamics, but this feature seems completely missing. I believe the disappearance coincided with this new version of Outlook that places the navigation icons for Mail, People, Tasks, etc. down the left-hand side of the window in a vertical sidebar, which is where previously you could launch the app from within Outlook. We used to be able to, for example, choose the "Add-ins" icon and launch the D365 app inside Outlook that way, but that option is no longer available. Clicking on "More apps" just brings up a pane to install more apps.

Even recent MS documentation on the subject refers to something that doesn't seem to even exist anymore. The following docs article:
Track Outlook contacts in Dynamics 365 for Outlook
states,
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In Dynamics 365 for Outlook, choose People in the navigation pane, and then select up to 20 contacts.
There is no such option for tracking in the People section as described.
Is this no longer possible? I am trying to on-board a new D365 user that would like to start tracking her existing (long list) of contacts in Outlook in Dynamics.
Thanks in advance,
Bob