The application runs inside of the Flatpak sandbox and therefore has a different mount namespace, PTY namespace, PID namespace, etc. That makes tracking foreground processes for simple things like "is the user running something when they close the tab other than the shell" extremely difficult. You'll just get 0 back a the PID from the TTY API.
Additionally, being able to monitor container APIs in the long run will require more than file monitoring a podman json file in the user $HOME. It could connect to a socket for monitoring (like machinectl, etc).
All these sort of things really benefit from running on the host rather than the UI sandbox.
> is said agent tied to prompt or could the "container detection extras" be usable with other Linux terminals
In that it's bundled with prompt, but it's just a D-Bus API albeit on a private socketpair(). The agent is not much code though to copy.