What? I thought every BMS is also a balancer!
Not necessarily. They are different devices. Sometimes they come in a single unit, sometimes they don't.
The job of a BMS is to provide several types of protection: overcurrent (including short circuit), overcharge, overdischarge, some will also do overheating protection. Cell balancing is strictly speaking a separate task, and it's not always considered to be required.
Yours however does have a bunch of resistors and SOT23 parts, and that might be a balancer, I can't readily tell this (maybe someone else can). Even if so, it will be a low-power one, and if it's there, it doesn't do a good job. What do the specs of your BMS say, if there are any?