Long time BirdNET fan, but I used the Merlin app for the first time yesterday and found it much more useful [0] It’ll display multiple bird species at the same time, and highlight which song belongs to which species in real-time. Recommend giving it a shot if you haven’t!
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.
BirdNET has some advantages -- it lets you select a segment of audio and it'll give suggestions, even if it's not extremely confident in those suggestions, meaning it can sometimes do better in noisy environments. Merlin is generally more useful, but the BirdNET app has its place for sure