Processes in Microsoft 365 for setting up Office apps, redeeming product keys, and activating licenses.
This is not something that a program update would cure. From your message, it sounds like you may have already read this page, but is the best guide available to troubleshooting corrupt documents in Publisher. Some steps have different names in 2013: Troubleshoot Damaged Publisher Document
This page is specific to documents containing OLE objects like embedded Excel, Word or PowerPoint files: Publisher Cannot Open the File
If you can't recover the document, here's how you can at least recover some data from it: Recover Data from Corrupt Publisher Document