Hi @Alex
If your groups are synced from on-prem AD to cloud, then you need to manage them from on-perm only rather than in cloud.
If you want to manage them from cloud/azure, you will need to recreate them in cloud and add members.
Some script could help you meet this need: Migrate Distribution Groups from Exchange On-Premise to Exchange Online
Please Note: Since the web site is not hosted by Microsoft, the link may change without notice. Microsoft does not guarantee the accuracy of this information.
And I will help you add the azure related tag in your post if you still need support from azure side, thanks for your understanding!