Installed Postgres.app but it won’t work

The psql binary for Postgres.app is inside the application bundle and you’ll have to add the appropriate directory to your PATH. From the fine manual:

Configure your $PATH

Postgres.app includes many command line tools. If you want to use them, you must configure the $PATH variable.

If you are using bash (default shell on OS X), add the following line to ~/.bash_profile:

export PATH=$PATH:/Applications/Postgres.app/Contents/Versions/latest/bin

[…]

So adjust your PATH setting in your zsh config files to include the

Contents/Versions/latest/bin 

directory inside your Postgres.app bundle.