If you select the Override all Salesforce sync settings for my team checkbox, you will see the option to either only allow logging via BCC or only via API.
If you choose API logging, all settings that are selected for Opportunities, Leads, Contacts will be set for the entire team after you click Save Changes.
From here, you will also be able to mass-enable Opportunities and Task Sync across the team.
Mass-enabling these settings will use a high number of API calls across your team's Salesforce settings.
1 – Enable “Configure my team’s settings”
2 – Enable Team-Wide Sync Settings
3 – Configure how you would like your email activity and most recent MSE activity to be logged to SFDC
4 – Enable “Sync Sales Connect Tasks” is optional
(note: MSE allows you to skip tasks while SFDC does not – so you have to decide how SFDC handles that skipped task)