npub18wjc0rvsha3vx3np96cc4sne0npsp7777v4nuwwaac4y3zhqnqgqfulvmv (npub18wj…lvmv) It is, as others mentioned, just called the “intro”. The jazz-specific version goes back to the beginning of #jazz, the beginning of the recording era, with a few distinct measures that just kick things off. The idea of using an entirely different melody and lyric, sometimes lasting many measures, developed in the next decades as the genre developed.
https://youtu.be/F-rzYsdRwgc?si=KgEJwrIo4oakmUtL