Just re-use your activation code like everyone else. (unless your installing another copy on another computer: which is a breach of license if your using it on two different computers. but the same restriction is present for running Windows 10 - so its' one you should be familiar with)
You bought the product acknowledging you agreed to use it as intended. Wolfram can't possibly know if you wish to "change computers" in the future to something un-supported. That's clearly outside of any store purchase scenario.
I sympathize with you, I wish I could transfer my 11.x license between an imac and win10 in seconds (dis-allowing the other computer to run at the same time). But I can't either. The problem is people steal.
You DO NOT need a system transfer license if your mac mini has to be re-installed. I can't say why. I might add I cannot verify that a STL is needed for re-installing WIN10. My guess is no: not unless you walked it to a different computer. (the license is clear you can only have one running installed copy per purchase)
If you speak to wolfram they might be happy to give discount on a second "home use" copy. MIght.
Mathematica is an excellent system it's well worth keeping on a "stable computer" (perhaps a mac mini) and leaving installed for continual use (rather than on a PC that is continually part hacked or continually requiring re-installation (win10? i didn't know that mine seems ok).
I used to be frustrated with it when I had a "PC from parts", but it was well worth it, and I keep it on a mac mini now.