Individual flatpaks are not installed with apt, so it cannot list them. To see installed flatpaks, run flatpak list.
(Installing a flatpak from the PureOS Store app will be using flatpak install invisibly, while installing a native PureOS app will be using sudo apt install.)
For listing your installed applications (and getting their package names), you might be interested in this thread, as well as the thread of Kyle’s that links from there. You can use the commands that those scripts use without creating the “apps” described in those threads, if you prefer.