Most of these changes are done through the Endpoint Manager.
Settings → Endpoint Manager → Burger Menu (on the right side of the page) → Sangoma → D&P series phones and then you edit the template that then gets assigned to an extension.
Not sure if the phone app on these ties to the contacts in the Contact Manager module but the template editor above does have the “APP-Contacts” as an available button assignment, which is what you see on your screen in that screenshot already.
Here is my template/model settings for P320 phones. I found that users in groups had access to contacts disabled, I will see if this affects contact button.
Still not sure why only 1 speed dial displaying. If someone from Sangoma can explain?