Hello Star_Lord,
Distribution Group is mainly for distributing emails, while SG is mainly for assign permissions.
For Transport rule in EAC, if your main concern is to control mail distributing, I think DG is fine:

Create and manage distribution groups
Manage mail-enabled security groups
I personally don’t suggest you use Office 365 group for transport rule, for you’ll find that you can’t add Office 365 groups to some conditions in a transport rule.
If you have additional requirements, then you could also upgrade current DG to Office 365 group, or create Office 365 group directly:
Why you should upgrade your
distribution lists to groups in Outlook.
Here’s more details about transport rule with some specific templates you can refer to:
Mail flow rules (transport rules) in Exchange Online.
To delete Office 365 group, if group owner is end-user, he or she can delete it in Outlook desktop app as well as Outlook web app:
Delete a group in Outlook. Admins can remove group directly in either Exchange admincenteror Office 365 admin center.


Above methods can soft deleted a group, admins can restore it within 30 days. If you want to permanently remove group, kindly refer to this article:
Permanently delete an Office 365 group.
If you have any concern, feel free to let me know.
Kind Regards,
Anna