Explanation
AD groups can control public group assignment, role assignment, and permission set assignment through Identity Connect. Identity Connect is a tool that integrates Microsoft Active Directory (AD) user accounts with Salesforce user records1. It allows Salesforce admins to leverage the existing user data and group memberships in AD to automate user provisioning and deprovisioning in Salesforce. Identity Connect can map AD groups to Salesforce public groups, roles, and permission sets, and assign them to users based on their group membership2. This way, AD groups can control the access level and visibility of users in Salesforce.
AD groups cannot control granting report folder access or custom permission assignment through Identity Connect. These are not supported features of Identity Connect. Report folder access is controlled by the folder sharing settings in Salesforce. Custom permission assignment is controlled by the custom permission settings in Salesforce. References: Get to Know Identity Connect, Map Your Data, [Folder Sharing], [Custom Permissions]