Does your implementation require response with the newly created case ID to remote system?
If it doesn't, I'd split the functionality into two different classes and do something like this:

@RestResource(urlMapping='/insertCaseWithAttachmentRestService/*')
global with sharing class insertCaseWithAttachmentRestAPI {
    //In this method we insert case with multiple attached files
   @httpPost
    global static void insertCase(caseRequest req){
      
        ReqToCaseService rcs = new ReqToCaseService(req);
      
        System.enqueueJob(rcs);
    }
}


public with sharing class ReqToCaseService implements Queueable
{
  private caseReqeust req;
  
  public ReqToCaseService(caseRequest req){
    this.req = req;
  }
  
  public void execute(QueueableContext qc){
    convertReqToCase();
  }

  public static Id convertReqToCase(){
        Case caseObj = new Case();
        caseObj.Product__c = req.pdt;
        caseObj.Type = req.type;
        caseObj.Status = req.status;
        caseObj.Origin = req.origin;
        caseObj.Subject = req.subject;
        insert caseObj;
        
        List<Attachment> attList = new List<Attachment>();
      
        for(attachmentRequest att : req.attList){
            attList.add(new Attachment(Name=att.attachmentName, 
                                      Body=EncodingUtil.base64Decode(att.blobString),
                                      ParentId=caseObj.Id
                                      ));
        }
        insert attList;
        
        return caseObj.Id;  
  }
  
  //Wrapper class
  public class caseRequest{
        String pdt {get; set;}
        String type {get; set;}
        String status {get; set;}
        String origin {get; set;}
        String subject {get; set;}
        
        List<attachmentRequest> attList {get; set;}
  }
  
  public class attachmentRequest{
        String attachmentName {get; set;}
        String blobString {get; set;}
  }
  
  
}