The technology Google is using here is very different. They also have active detection on Assitant, but this one is a passive 24/7 detection. There's a local database of the ~10k most popular songs, and it's only ~50mb [0]. It's all done locally, and when it works (Which is very often), you just have to look down at your phone and the song name is already there on the lockscreen without you touching anything.
As mentioned above, this is already running to do OK Google detection. It's also not scanning 100% of the audio, as far as I understand, it analyzes samples roughly each minute. I'm sure they would not make this a feature if it had a big impact. From my own experience, turning this feature on or off made no difference in battery life.
[0] https://www.xda-developers.com/google-pixel-2-now-playing-so...