It's "functional" because the chords in the harmony have the function of establishing key centres, moving towards and away from them, establishing transitions to remote key areas etc.
One of the best technical books about functional harmony is "Structural Functions of Harmony" by Arnold Schoenberg[1], which is much shorter than his "Harmonielehre" but really packed with interesting detail about key and chord relationships.
[1] Yes that Schoenberg but this isn't about serialism, it's about trying to explain all the harmony up to and including Mahler. Here is an online pdf of an early edition https://is.muni.cz/el/1421/podzim2007/VH_53/Schoenberg_Struc...
@tonaljs/key gives you some specifically functional info, but the vast bulk of it as useful for non-functional analysis – though it does assume 12-tone equal temperament.