What you may want to do is simply use your old mac mini as a computer on your (home) network. My understanding is that you aim to store stuff you want to access, just luke an external drive.
Indeed, that old mac mini could serve a purpose of storing stuff (basically actung as a server). No need to have a monitor on it (perhaps just to set it and make it part of your home network). Then at any time, from your newer mac you could access soecific folders, edit files, move them back and forth, or just store.
Not the most optimal use of a computer (tasks you could simply do with external drives), but certainly better than letting it go for peanuts, unless you eventually wish to give it as a gift to family member.