Though auto-takeoff and autoland (in addition to the cruise autopilot) have actually existed for many decades, making it theoretically possible for an aircraft to have every phase of flight automated, this isn’t really done in practice.
Autopilot isn’t a single thing. It’s an umbrella term for dozens of discrete automation functions that can be used all at once, or none at all, or in any combination. So things like auto-navigation (automatic turns), auto level (maintain flight level), autothrottle (maintain speed), auto brake (on landing) etc. But tons more are automatic safeguards, like stall prevention.
In this case, they added another computer-controlled automatic adjustment to compensate for the different lift characteristics of the MAX, to make it behave like a classic 737, so that a pilot doesn’t have to be completely recertified for a different aircraft type, which would be needed if it handled differently. The problem is simply that they didn’t even mention this new system to pilots, never mind explain how to disable it when faulty sensors are causing it to make erroneous corrections, as happened with Lion Air and may have happened with Ethiopian.
Back to your question: no flight is ever under total computer control. Far from it. The pilots are coordinating the bazillions of different settings and modes, some manually, others through automation. The programming is critical (like, you must correctly enter the flight plan, so that auto nav knows when to turn). And a flight is never flown according only to pre-decided steps: air traffic control is directing them what to do, when to do it, etc. So for example, you may choose to use auto level at cruise, but you’re still in contact with air traffic control, who tell you which flight level to use, and you must enter that into the autopilot yourself, and ensure it’s in a mode that allows it to change flight level.
People mistakenly think that pilots don’t do anything. But in fact, aviation is extremely demanding, with tons of tasks that must be done without fail. And so offloading some of the workload to the autopilot makes total sense. But pilots also want to fly. They didn’t do all that training and spend years earning poverty wages as junior pilots only to then sit in the cockpit and do nothing. So often, they do many things manually that they could automate. And other things, like takeoffs and landings, are never done automated, even if the hardware and software is present. They’re there as backup systems if, for instance, a pilot is incapacitated and the copilot is also occupied with some emergency and needs to offload a task.