You said it very well yourself.
From a technical standpoint, tapping in uses NFC, which doesn’t require any power on the band itself. NFC works by the tapstyle generating a magnetic field which powers the MB when it is in close range, which in turn uses that power to transmit the MB ID information back to the tapstyle.
Anything that detects the MB remotely (specifically, Photo Pass) uses Bluetooth Low Energy, which requires (very little) on-board power. Typically, this means it can last about 2 years, give or take.