Solution:
From learning.sap.com, in the lesson “Creating Logical System” under Configuring Global Settings in the Administering SAP Integration Suite, Managed Gateway for Spend Management and SAP Business Network learning journey, the purpose and use of the logical system created during the global settings activity is explained:
“The logical system value you add in this configuration step … will be used by the Interface Setup Integration program for automatically creating outbound parameters for outbound IDocs in the Partner profile (WE20) settings for Partner Type LS (Logical System).” SAP Learning
This is also reiterated in the “Analyzing Required Configurations” lesson, stating that:
“The value created here will be used in Interface Setup program for generating outbound parameters of Partner Profile under TCode WE20.” SAP Learning
Based on these sources, the correct answer to your question “When does the value of a logical system created during the Global settings activities get used?” is:
•C. While executing the Setup the Interface program in the Managed Gateway-AddOn
It is not used in the other options listed (creating a connection, maintaining cross-references, or creating logical ports in SOAMANAGER) according to the learning.sap.com documentation.