why does turning on and off the send copies of group conversations and events to group members work?

Hello, you can read more about it here https://docs.microsoft.com/en-us/microsoft-365/admin/create-groups/manage-groups?view=o365-worldwide#send-copies-of-conversations-to-group-members-inboxes as you'll see it's default when using admin center but you can enable it, and users can opt out if they like.

When it comes to controlling the settings you can use PowerShell and the following cmdlet

https://docs.microsoft.com/en-us/powershell/module/exchange/set-unifiedgroup?view=exchange-ps

https://docs.microsoft.com/en-us/powershell/module/exchange/add-unifiedgrouplinks?view=exchange-ps

These articles describes how you could use them

https://office365itpros.com/2020/10/21/update-teams-send-meeting-invitations-to-members/

https://office365itpros.com/2020/06/02/teams-schedule-meetings-teams/

Look for these
-AlwaysSubscribeMembersToCalendarEvents
-AutoSubscribeNewMembers
-LinkType