Migrating Distribution Lists to Outlook Groups

My recommendation is to avoid doing this type of migration just for the sake of it. Distribution groups are still a viable solution and as long as they do the task you should stick with them.

If you need some of the additional functionalities Groups offer, sure, go for the migration. You can use PowerShell to script the nested DGs scenario, but due to the limitations of Groups, you will have to "flatten" the membership. Also, remember that Groups are not a security principal, you cannot use them to assign permissions. Well, neither are DGs, but I imagine you probably have some mail-enabled security groups in the mix.