The duplicate rule can be captured by the errors thrown at insertion as follows.

Insert and capture error

Class__c classToCreate = new Class__c(Name='Science', Grade__c=8);

Database.SaveResult saveResult = Database.insert(classToCreate, false);

if (!saveResult.isSuccess()) {
 for (Database.Error error : saveResult.getErrors()) {      
        if (error instanceof Database.DuplicateError) {
                    
            Database.DuplicateError duplicateError = (Database.DuplicateError)error;
            Datacloud.DuplicateResult duplicateResult = duplicateError.getDuplicateResult();
    
            System.debug(duplicateResult.getErrorMessage());
            
            Datacloud.MatchResult matchResult = duplicateResult.getMatchResults()[0];
            Datacloud.MatchRecord[] matchRecords = matchResult.getMatchRecords();
            
            for (Datacloud.MatchRecord matchRecord : matchRecords) {
                System.debug('MatchRecord: ' + matchRecord.getRecord());
            }   
        }
 }
}