Just to clarify - the article describes BirdNET-Pi, not the mobile app Birdnet. In the mobile app we have to record and manually select a fragment to analyze, here it's a continuous monitoring where detections are visible in real time and can be replayed.
OP explains all that admirably in the section entitled: "Terminology: BirdNET vs BirdNET-Pi"
I use both. I have a BNPi at home in our summerhouse with a mic on the outside. We live next to a park and the bird song can be deafening in summer!
I have the Birdnet app on my mobile and its ideal when out walking to do a quick survey or identify a song I don't recognise.
Whilst I'm commenting here, I'll drop a shout out for the "Flora Incognita" app for plant identification.