As far as I understand it, upgrading to Catalina will not change your shell (by default, currently bash), only creating a new account (or installing Catalina fresh and not migrating) would result in using zsh.
Catalina is only changing the default shell, not your current shell.
Ironically, I used to use zsh decades ago, but eventually got tired of having to install it everywhere and gave up and used bash, and only in the last couple years have I actually fully committed to bash. Timing, right?!
Whether switching the zsh is an “upgrade” or not is an open question - it is different, but not necessarily better.
In any event, this wont affect the Execute a Shell Script action since it uses /bin/sh to execute the script, which you may start with #! to explicitly specify what shell or language to run, but that is all handled by sh.
So if you want to write your scripts for zsh, just start them with #!/bin/zsh, which should work for any recent version of OS X.