DIY water meter magnetic sensor

My water meter is compatible with the Flume, so I think it has a rotating magnetic disk inside. It doesn’t have any other visual rotating dials to monitor, and the digital display requires activation with a light. So magnetic field sensing seems like the way to go if I want to monitor it.

After reading through other people’s projects, I’ve identified two magnetic sensors that seem to have good results for other people:

Wondering if anyone has gone through the rabbit hole of water monitoring and can give any advice on what sensor to use? My meter looks like this. I don’t know what that black thing on the left is, not sure if that’s something I can use to monitor. The circular part looks like what most people have for their water meter.

If meter has plastic body, hall sensor could be option.
Did you try if your phone’s magnetometer can detect the dial?

Didn’t think to try to use the phone’s magnetometer. I’ll see if there’s an app to help with that.