This isn't a third film in the series, but a film based off the books and not directly related to the Chevy Chase ones; there's not only no reason why Faltermeyer should be hired, there's no reason to use his theme. Just like if a new Conan the Barbarian film unrelated to the Arnold films came out, there's no reason to use Poledouris' theme.
oh! but they use exactly chevy's movie font for the title
That's actually the font from the original novel series cover art.
Arnold's tracks are not jazz music! They are rock and roll, with funkey keyboard grooves
Last track is very "big bandy", I think. The others might be more funk than jazz, but funk was always jazz-adjacent. I don't hear any rock'n'roll in them.
Regardless, the point was that I had hoped for an electronic score (perhaps seeing Arnold return to his old roots of the 90s JB movies, with those neat electronic interpolations), but too much to hope for, I suppose.