A battery pack on a modern EV is typically just a bunch of cells wired together in series, or a bunch of parallel groups of cells in series. There isn't anything to cause power to be pulled from one group of cells versus another -- if that happens, it's a problem because it would cause the cells to get out of balance. (You'd typically have a "battery management system" whose job is to monitor cell voltages and bleed off little power from cells that are reading too high to keep everything properly balanced. But that happens very slowly, and at low voltages and current.)

As far as the motor controller is concerned, the battery might as well just be a single cell. If you change to a different kind of battery, you might need to change some of the motor controller's parameters (like maximum current limit) if those were designed around the limits of the old battery.

edit to add: when it comes to the charger and BMS, that stuff might or might not have to be replaced depending on the extent to which it can be made to work with a different configuration. And just like replacing an engine in a modern gas-powered car, there's probably a host of sensors that will trigger a whole host of warnings if they aren't reconnected to equivalent new sensors or spoofed in some way.

The part which deals with all this is the battery management system, and it's almost always integrated into the battery itself, for reasons of practicality, safety, and seperation of concerns. Its interface to the rest of the car and charging system is fairly straightforward: mostly it just needs to report state of charge and current limits for charging and discharging (chargers for these packs are rarely anything more than a constant current supply being controlled by the BMS). It can in theory provide more detailed information but this is just diagnostic, not something the user or any other part of the system can really take action on (for example there's no way in current EV packs for the motor to draw from specific cells more than the others).

Basically the only way for car manufacturers to make this interface hard to replicate with third-party packs is by introducting some kind of DRM-like signatures on the messages from the BMS.

The question is whether the necessary brains are part of the pack or part of some other component in the car. But in any case, if we require the specs to be open, third parties can build compatible batteries.