The last part is interactive and I would like to avoid that.
Is there an alternative to using /usr/pgadmin4/bin/setup-web.sh ? I would prefer to just copy some pre-configured config files into the container.
Which would I need to copy?
The setup script doesn't create any configuration files you can just copy - it enables Apache HTTPD and some required modules, and if you're on Redhat it will run some SELinux commands.
You can avoid the interactivity by setting PGADMIN_SETUP_EMAIL and PGADMIN_SETUP_PASSWORD in the environment to an appropriate email address and password for the initial user, and then running the script with the -y option on the command line.