I think I wanted this as a "backup" in case my chest should ever break because I spent lots of time building a big filter list for loot box opening.

Maybe use the paper item to store data onto it, then extract the text data through nbt or some shit to reapply the filter? No idea I am not a coder, but maybe the paper idea might be good. You can store the settings onto a paper, then reapply them by reading the text of the paper.

Thinking of adding a filter library to allow for persistent filter settings:

• Filters you can configure (Name Filter, Preset Filter, etc.) get a "star" button you can toggle on their GUI
  
• Filter menu gets a "Library" button which opens up a Library of all Filters you have saved, where you can also manage them (rename, duplicate, delete)
  

Benefits: No weird item handling for moving data around, easier to setup sorting networks, no accidental loss of sorting config (e.g. Creeper)