I tried many apps, it doesn't show in betterbatterystats, os monitor, the shell "top" command, dumpsys, etc. Battery calibration, the *#0228# code, etc, etc.
The battery doesn't have any visible damage, but it does spin (I've read the spinning test is bullshit, so I don't trust it too much).
I think the phone is 2 year old, but the battery label say it was manufactured in 2013.