See/read Mac mini hard drive from MacBook Air?
Allan’s response makes sense to me. I have been pretty successful retrieving files from Mac Minis using a USB to SATA adaptor. I use a Newer Technology USB 3.0 Universal Drive Adapter https://www.newertech.com/storage/

For guides to extracting the drive from the Mini, I rely on iFixIt. https://www.ifixit.com/Search?query=Mac+mini+drive

Denny