move items to a new list? With attachments?

In fact, you can move attachments with REST calls, it is the same as moving a document.

The trick is that attachments of items are stored not in the item but on the list directly.
Let say I have list named "TEST", here's the attachment for the Item 2, you will find a hidden folder at the root of your list named "Attachments" and a subfolder with the ID of your item

/sites/Allan/Lists/TEST/Attachments/2/MyAttachedFile.txt
-->
{ServerRelativeUrl}/Lists/{List name}/Attachments/{Item ID}/{File name}

If you move your file at this location, it will be considered as an attachement of the second item.
There also a second trick: You cannot use "copyTo" (from SharePoint API) directly to the destination folder if the folder does not exist beforehand. You need to create a dummy file (with content) to the the hidden folder location, then delete it. Otherwise your workflow will crash on the "copyTo" REST action.
There's also a 3rd trick: the size of your request cannot exceede 400 chars, but there's a workaround.

Please a look at this post : https://community.nintex.com/t5/Nintex-for-Office-365/Copy-task-attachments-to-Master-Item-on-O365/m-p/101874#M11905