What I noticed is, that the displayed maximum consumption in the status panel of any given Laser Turret grows when researching Laser Shooting Speed, in accordance with the bonus that is added, but not when they level up from HeroTurrets.
I'm also fairly sure, this is confirmable visually, as you can use the 'Electricity' bar in the status panel as a gauge on how frequently any given electric Turret fires, it's simply the times per second, the bar empties and fills up again.
I'm currently in a K2+Rampant run, where I buffed the default settings a little for the turrets to reach +100% everything on max level (5).
Energy per shot is 975 kJ with 2/s base shooting speed, the Turrets showed a maximum of 2MW power draw without any research.
Now with +100% shooting speed (researched) they list 4MW maximum consumption, which doesn't change when they level up. And as far as I can tell, the electricity bar empties and fills not more that 4 times a second, no matter the level.
And as a last metric you can watch the Electricity bar while a turret is firing: Normally the bar refills completely before each shot, from about 60% full directly after firing (meaning a Laser Turret has a buffer worth around 2.5 shots), since the internal buffer recharge rate is always larger (~20kW) than the maximum usage of the system, it's the same for Roboports or any structure that "uses" electricity, any unmodded structure anyways. However, levelled turrets drain their electricity faster due to the increased firing speed, which you can see by their electricity gauge quickly draining to 0 after a few shots, which then only reduces to 0 again after enough charge has been built up in the internal electricity buffer.
Or to put it short, for standard Laser Turrets the bar flickers around the full state, whereas for levelled turrets it flickers around the empty state, meaning the energy is consumed faster than it can be recharged, which in turn means the buffer recharge rate cannot keep up with demand and needs to be taken into account when levelling up electric turrets.
