After tweaking etc I found out the correct name format is

groups/<ID>

The name can be found with

$ gcloud identity groups describe gcp-developers@domain.tld
dditionalGroupKeys:
- id: ...
createTime: ...
description: ...
displayName: gcp-developers
groupKey:
  id: gcp-developers@domain.tld
labels:
  <http://cloudidentity.googleapis.com/groups.discussion_forum|cloudidentity.googleapis.com/groups.discussion_forum>: ''
name: groups/<SOME ID>             <--------- This is what you need
parent: ...
updateTime: ...

So you need the value in the

name:

field. Maybe the docs can be updated to make it more clear.