Jira Cloud does not support any third-party custom field type - not even via the new Forge-approach of Atlassian, which only renders on the new issue view but nowhere else in Jira. Therefore, I had to find another technical solution based on the limitations of the Atlassian Cloud in opposite to the on-premise versions of Server/DataCenter:
You have to configure the related Group Sign-Off fields in the global app config instead of native Jira custom fields because no Group Sign-Off custom field type can be implemented, currently. This configuration within Jira Cloud has to be done manually, once: an admin task (have a look at the cloud features at https://polscheit.atlassian.net/wiki/spaces/GSO/pages/693895177/Administration+Jira+Cloud: major features are the same like for on-premise but there are some minor differences, e.g. accountIDs instead of username/key due to GDPR).
Depending on their complexity of your logic rules these can be taken over 1:1 or you might have to adjust them a bit according to the documentation „Administration Jira Cloud".
Having properly configure Group Sign-Off in the new Jira Cloud instance, the process of importing GSO-fields from Server/DataCenter into Cloud is easy and described on the tab „Importing“ for the cloud app:
If you need additional help, please do not hesitate to contact me at firstname.lastname@example.org.