1. https://answers.microsoft.com/en-us/msoffice/forum/all/savin...
2. https://community.fabric.microsoft.com/t5/Service/End-User-S...
In both cases it's being used for "copying".
We can also see it was used as early as 15 years ago on this very site ( https://www.hackerneue.com/item?id=1182478 ), so it's not a new turn of phrase.
My experience has definitely been that I've heard it more online and in San Francisco, and not very often in Germany, Texas, or Russia. Are you in one of those areas?
I feel like the etymology is something like "print off a few sheets" becoming "copy off a sheet with the copier", and then to the more general digital copy meaning.
Conceptually, I think that the "off" serves the purpose of aligning it with something like "split off"—you're essentially forking the history by creating a separate saved copy.
this is a strange turn of phrase