Can I read the code?
Yes. The code of the app, the agent and the platform is public, under the Apache 2.0 licence with the Commons Clause: you may read it, change it, build the agent yourself and run your own platform. The one thing the licence forbids is selling Pupitre, or a service built mainly on it.
You do not have to read the source to know what the agent did to your machine. Everything it installs is standard software, configured in ordinary files you can open, such as /etc/ssh/sshd_config.d/10-pupitre.conf or the Caddyfile. The documentation says what every module installs, changes and removes.
What the licence allows