Great Question....
The on board systems will let the pilots know when they think a 'step climb' is recommended. It bases this on the weight of the aircraft, and speed schedule that the pilots have programed.
But onboard computers are only as good as the programmer that wrote their system, and the information that they have been subsequently given.
So if the pilots are aware of turbulence at a higher level, or unfavorable winds at a higher level, or there are traffic or airspace issues, then they will manage the flight as required. And climb or descend as appropriate.
At no time is the aircraft able to climb or descend without deliberate pilot input.
This includes aircraft conducting an 'autoland'. The aircraft is not able to deploy the wing flaps, or the landing gear, without the direct input and judgement of the pilots.
Keep the great questions coming!