Usually the BMS in such packs does have control over the flow in and out of the battery: it can isolate the connections if there's an overcurrent or over/underv

Usually the BMS in such packs does have control over the flow in and out of the battery: it can isolate the connections if there's an overcurrent or over/undervoltage (or overtemp). That's usually the main contribution to safety. And it's also pretty typical that the BMS is what defines the charging profile: the charger basically just follows instructions from the BMS (and if it doesn't, said isolation comes into play as protection). This doesn't necessarily all happen on one chip: in the larger packs this is likely distributed between a few different components, including a chunky contactor for the isolation.