ScriptRunner's Group Picker Searcher subclasses Jira's own GroupPickerSearcher class, which converts group names to lower case before storing them in the index. However, it searches the index case-sensitively, which means that group names containing upper-case letters will not be correctly found.
This problem does not occur for regular group picker custom fields because they are all indexed by MultiGroupCFType.MultiGroupCustomFieldIndexer, which stores group names in the index as-is without normalising the case. Note that despite being called MultiGroupCustomFieldIndexer, this indexer is used for both single- and multi-group picker fields. We should do the same.
It is possible to work around the problem by using the Multi Group Picker Searcher instead: this necessitates also switching to the 'Group Picker (multiple groups)' template and wrapping the output of the field's script in a singleton list.