Thanks @szymon_dybczak I have asked about it in the github thread.

I was able to successfully manage AlertsV2 permissions using the Workspace Permissions API with the correct object type:

workspace_client.workspace.set_permissions(
    workspace_object_type="alertsv2",  # Key difference: use "alertsv2" not "alerts"
    workspace_object_id=str(alert_id),
    access_control_list=[
        AccessControl(user_name="user@company.com", permission_level="CAN_MANAGE")
    ]
)

The solution was using workspace_object_type="alertsv2" instead of "alerts". This works for the new AlertsV2 system.