BMS’s support charge and discharge.
If you’re going to avoid connecting discharge through BMS and connect your load directly from battery and using the BMS only for charging, it is preferred that the BMS can handle by few amps more than your charger can push into Battery. so for example, if your charger can charge max 4A so its better to get a BMS that can handle 6A.
Regarding to the chargers, most of the chargers in the market come with protection circuit, so they automatically cut off the power when the battery’s voltage becomes equal to charger’s voltage. but if the charger doesnt have a protection circuit, then the BMS should handle cutting the power when the battery voltage gets equal to charger’s voltage. by using a cheap BMS its better to keep an eye on testing it when running at the first time just to make sure everything is working as expected.