I received the sensor and wired it. It turned out more difficult than anticipated to convert the signal into a meaningful current.
When plotting the signal, one can notice that when the current consumption increases, the peak AC voltage from the sensor doesn't increase. Instead, the peak to peak value increases.
Overall, it turned out to be easier to measure the peak to peak value (Vpp) without any conversion. It works perfectly in this case because we're not interested into the RMS value per se but rather the relative value: Is the AC switched on, and is it consuming lots of current or not ?
The updated code (production.ino) takes care of that. I need to run more live tests but so far everything is working as it should be.
Here's a demo of the unit working: