How to translate Groups in a multilingual site?
Your question appears to be somehow related to this issue, which is closed and fixed. That issue contains an image which looks like so:



So check if the version of the Group module that you're using, includes the patch included in that issue.

If you don't have it included, it's probably why you don't have a "group content type" translation option in /admin/config/regional/config-translation. And if you do have it included, go checkout that translation option to see what happens.