Are you asking about the helm master switch or the Perko switch near batteries? If helm master switch, I just think of it as sequence. Nothing’s on when starting the motor (including the helm master switch), so all power is on the motor starting. Once that’s in operation, and consequently the alternator doing its thing, then other items and accessories can be flipped on, so turn on the master switch, pop on the radio, etc… The helm master switch is a short cut to help stop battery drain by basically cutting most all electronics off from a parasitic battery draw when not using the boat while the Perko switch is still in 1, 2 or 1+2 battery position. It is not intended as an emergency stop engine and turn batteries on item.
And yeah, battery wouldn’t be part of any motor warranty issue, so steering you back towards the dealer and/or Bennington makes sense on that one. Isn’t your boat new, like a 2024? If so, and if you have a bad battery out of the gate, I think that is a legitimate warranty inquiry. Batteries fall outside of the warranty most all of the time due to them being a wear out item, but being a brand new boat (if I am correct on that) would be a very different matter in my mind. I think this might be particularly true if the dealer is saying the battery is damaged or not right in some way (open circuit?).
Also, good job following up on that specific battery they are putting in to make sure it’s what is recommended for your specific Mercury motor. Based on cost and what not, I am confident it is the right battery, but better to verify.