They fall under “something else” for sure. Footnotes are objects, just like text frames, rectangles, documents, and find/change sets, and have loads and loads of properties. Normally, I would write a script to copy all of the settings one by one, but … footnotes sure have a lot of them.
So I wrote an entirely new sort of script
It tries to copy intelligently whatever it can, from your currently active document (which should be in front of you), to either one single document of your choice, or to all open ones. In your case, you should open all of the documents in your book, then make sure the “source” for your footnote options is in front, and then run my script.
It may display an alert telling you what items it cannot copy: not everything in the destination options can simply be “set” to the equivalent value in the source document. For example, if you created a custom character and paragraph style for your footnote options, there should be one with the same name in the destination documents. The same goes for colors and stroke styles.
The script only copies the names of these objects, not their definitions! So if you used a stroke color “MyOwnSpecialColor” that is defined as blue in your source but purple in one of the other documents, the color will not change.
The script is a bit too long to post in-line so d/l it here: ftnoptcopier.jsx (alternatively, download directly from my site: https://www.jongware.com/binaries/ftnoptcopier.zip)
Download (use a right click and select “Save target as”, or equivalent) and move it to your User Scripts folder. Double-click to run — well, after opening all documents you need to adjust, that is.
(After trying it: it seems it gets a .txt added to the file name for free. Remove this, it should simply be “fntoptcopier.jsx”, otherwise InDesign Does Not Compute.)