Okay, I re-read the OP and I think
my confusion is caused by my car having a different automatic transmission design than your car?
I have an e-CVT in my Toyota; it's a belt-less design that uses a planetary gear and two electric motors (one has a double function as a generator also, because it's a hybrid). As @Thorgalaeg
says, it feels like driving a car without a transmission; like a bumper car in an amusement park or a fully electric car. You control the car with the pedals and your right foot. So, I always have power by just pressing the accelerator, or decrease speed in a turn with the brake pedal; no need to ever touch the gear lever. It doesn't have '1-2-3' gears to choose; just D and B for engine braking (I never use that one).
It sounds like your transmission has fixed gears and it down- or upshifts between them - and you can feel that as the driver. You don't have that with an e-CVT, so that's why your experience is 'new' to me.