Other factors play into it more. Slight thrust adjustment can change it more, lift, attitude, altitude...
Thrust isn't normally adjusted for this. Aircraft have trim which is adjusted. Autopilots frequently adjust trim but some directly adjust control surfaces. In either case, pilots adjust trim for a variety of reasons. Most commonly is altitude tweak and fuel burn.
As fuel burns the weight is reduced. This frequently changes center of gravity. Which changes angle of attack. Tweaking with trim changes angle of attack which reduces drag. In turn improving speed.
I was intentionally using something not normally done for the purpose of control to show it has an affect on control.
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