I think what you are seeing is not a native feature of Jira Server but rather something that has come from a third party app added to your instance.
Natively Jira has the concept of Components within projects which ties to a multi-select field in the issues, but not versions of those components.
Natively Jira also has the concept of Release Versions associated with projects.
But it does not natively have the concept of Component Versions, as far as I know.
In trying to find information via internet search on this topic I found that there were issues in Atlassians backlog for this feature, but they have been marked as "Won't Do".
I also found a company that offers a plugin for this, but the screens in the demo don't match what you shared.
https://jexo.io/blog/how-to-track-component-releases-in-jira/
I also found a reference to this plug-in
https://marketplace.atlassian.com/apps/1211825/configuration-management-toolkit?tab=overview&hosting=datacenter
Can you have a Jira Admin look through the plug-ins added to your instance to see if there is a plug-in that is accounting for this added functionality? Since I believe it is not native, then the JIRA REST API would not include information directly calling out how to access the data. You would need to query the vendor of the plug-in to get information on how to get that information.
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