When you use the manual crank, it bypasses the motor. What your dealer is calling an actuator, who knows. The manual crank directly rotates the pinion gears on the cross shaft. When that cross shaft spins, that drives the rack gears in and out to extend and retract the slide. It is a VERY simple and reliable system.
However, if the dealer did not adjust the slides properly before you took delivery, and you drive the RV around, the kitchen slide probably moved a bit and caused it to jam. Moving it 1/4" freed it up so it could move again. 1/4" isn't much so now you know how accurate things need to be.
Your RV should have came with Lippert manual on the slides. Read that manual to understand how slide mechanisms work and how to adjust them. Pushing a button and it not having things work sucks I know. An RV has tons of systems in it. When it is raining out and you are stuck inside, grab your favorite beverage and read just one manual. Reading manuals is boring and confusing. But not knowing what is wrong is even more so. Lots of manuals are online if you prefer the PDF version vs. paper.