Hello my friend,
I was facing this same challenge, and testing some possibilities I’ve found what we need.
All the custom type fields “com.atlassian.jira.plugin.system.customfieldtypes:labels” was a mystery because the options didn’t appear on labels or any other field option API.
Using this endpoint:“/rest/api/3/jql/autocompletedata/suggestions?fieldName={FieldName}” (https://developer.atlassian.com/cloud/jira/platform/rest/v3/api-group-jql/#api-rest-api-3-jql-autocompletedata-suggestions-get) we got all data suggestions just the way it appears on screen.
Best regards.