Supposedly MA does, but in my experierence doing it after your computer is already set up does not work so well (Just my experience - YMMV) - I had issues trying this for a selected few apps etc where it affected other items and ended up doing a complete new install to fix it
Easy enough to transfer the music - just copy the tunes folder complete into the Music folder in Catalina and then open music while holding down the Opt key to point Music to media folder and import / create a new Music Library.musiclibrary file
for apps you may need the latest version anyway for Catalina? so a freash install for a few apps does not seem too difficult?
I am not knocking migration assistant - it is awesome for transfers during an initial set up and I use every-time I replace a drive / OS / or new computer - great utility ?