I have read all Google documentation on managing and creating libraries, yet I still do not know if they are an appropriate option for the problem I am trying to solve.
besides making an add-on (already covered in another answer) I will answer your libraries question. They will work for you. What you are missing is the "connect" part.
For this you want to trigger the library code from say, onOpen. The onOpen in the library is not enough and not detected by apps script. Instead each of your spreadsheet's script needs an onOpen(e) which just calls yourlibrary.onOpen(e).
since those "hook" calls rarely change, specially once you stabilize your library api, and using it in "development" mode will let you modify just the library.
whenever one of those hooks needs to change (say a callback from an html GUI needs a new parameter) you need to update all the spreadsheets. to avoid this, make all your callbacks receive a single json object instead of multiple parameters.