Processes in Microsoft 365 for setting up Office apps, redeeming product keys, and activating licenses.
I did something similar and it all works for me.
Was getting the "Something went wrong" message, which brought me to this thread. Tried to Repair Office, no response (presumably because clicktorun is hosed). So I rolled back the 11th June updates. At this point Office 2013 was at 15.0.4623.1003 I'm guessing it had updated prior to Windows Update. Installed the Windows Updates again (one by one, I wanted to see which was the offender) Reboot and tested Office each time. Updates installed on Win 7 Pro 64bit (32bit Office 2013 + Office 2007 Access Runtime) as follows and in order:
KB2957689 - IE10
KB2939576 - Win 7
KB2957189 - Win 7
KB2957503 - Win 7
KB2957509 - Win 7
KB2965788 - Win 7
KB2800095 - Win 7
KB2952664 - Win 7
KB890830 - MSRT June
KB2878233 - Office 2007
KB2881069 - Office 2007
At no point did I uninstall Office or run the Fix It suggested by the Microsoft chatbot in this thread.