App Script to generate a PDF version from a google doc, preserving the PDF file link

code.js

function createPDF() {
  // Get the current Google Doc
  const doc = DocumentApp.getActiveDocument();
  
  // Get the document ID and name
  const docId = doc.getId();
  const docName = doc.getName();
  
  // Get the folder where the document is located
  const file = DriveApp.getFileById(docId);
  const parents = file.getParents();
  
  // If the document is in at least one folder
  if (parents.hasNext()) {
    const folder = parents.next();
    
    // Create PDF blob
    const pdfBlob = DriveApp.getFileById(docId).getAs('application/pdf');
    
    // Determine the PDF filename
    const pdfName = docName.toLowerCase().endsWith('.pdf') 
      ? docName 
      : `${docName}.pdf`;
    
    // Search for existing PDF with the same name in the folder
    const files = folder.getFilesByName(pdfName);
    
    if (files.hasNext()) {
      // If PDF exists, update its content using Advanced Drive API
      const existingPdf = files.next();
      const existingId = existingPdf.getId();
      
      // Store the sharing settings
      const sharingAccess = existingPdf.getSharingAccess();
      const sharingPermission = existingPdf.getSharingPermission();
      const isPublic = sharingAccess === DriveApp.Access.ANYONE || 
                      sharingAccess === DriveApp.Access.ANYONE_WITH_LINK;
      
      const resource = {
        title: pdfName,
        mimeType: 'application/pdf'
      };
      
      // Update the file content
      Drive.Files.update(resource, existingId, pdfBlob);
      
      // Re-apply sharing settings
      const updatedFile = DriveApp.getFileById(existingId);
      if (isPublic) {
        updatedFile.setSharing(sharingAccess, sharingPermission);
      }
      
      DocumentApp.getUi().alert('Existing PDF was updated successfully with preserved sharing settings!');
    } else {
      // If no existing PDF, create a new one
      const pdfFile = folder.createFile(pdfBlob);
      pdfFile.setName(pdfName);
      
      // Set default sharing to "Anyone with link can view"
      pdfFile.setSharing(DriveApp.Access.ANYONE_WITH_LINK, DriveApp.Permission.VIEW);
      
      DocumentApp.getUi().alert('New PDF was created successfully with "Anyone with link can view" permissions!');
    }
  } else {
    // If the document is not in any folder (i.e., in root of Drive)
    DocumentApp.getUi().alert('Document must be in a folder to create PDF');
  }
}

// Create a menu item when the document opens
function onOpen() {
  const ui = DocumentApp.getUi();
  ui.createMenu('PDF Tools')
    .addItem('Create PDF', 'createPDF')
    .addToUi();
}

you have to enable 'advanced drive api' to make this work. See
https://developers.google.com/apps-script/advanced/drive

Specifically follow the link here that says:
This is an advanced service that must be enabled before use.