I'm not seeing any BMS here. Looks like the last picture shows that you unsoldered the red/black wire from the battery which goes to the rear of the pack, where you probably have a tail light, a charge port, and maybe an on/off switch?
Based on batteries I own, there ought to be at least four wires between the rear part and the cells.
(1) Battery power (2) ground (3) charger ground (4) battery ON. You're only showing the red/black which are the first two.
That would suggest the BMS doesn't use an on/off and the cells are always on. The blue wire could be the on/off circuit to the controller to turn it on. If that's true, this design always gives you live power at the plug. Seems unsafe. Now if there's more wires you didn't show coming from the rear piece that goes to the battery, then I am wrong here.
Also if there are only two wires going to the cells, the pack would have to charge and discharge thru those two wires. It can be done, but it would complicate your selection of a BMS. Many have separate return wires for the power and the charge connectors,
Anyway, these pictures have not have not unveiled the BMS and do not give the viewer a clear idea on how this pack is connected.