I assume this isn't intended, since Metabolic Generator has a small built-in power capacity to not waste food. What I assume happens, is the Metabolic Generator only provides power if there is more than 25 spare power capacity. If I'm right, the easiest solution would be to change its capacity from 25 to 50.

I also thought that the builtin power capacity would give a sort of "buffer" like a battery does but it doesn't. Died due to cardiomechanical pump losing power. With internal battery or marrow battery installed, even if your power drops to zero, the metabolic generator keeps the most essential systems working with certain priorities. Cyberlegs, cybereyes and cardiomechanical pump will always retain power. If cyberarms are also installed, they take priority over cyberlegs and you can't walk (might need to be looked into?). I was hoping that the metabolic generator's built-in battery would function the same as installing another battery, but it does not.

There's no built-in batteries in generators, otherwise there would be no reason to have batteries. There's a 1 second buffer between generators and consumers, any surplus after 20 ticks is stored in batteries or lost forever.
Power consumption doesn't prioritize implants, it takes them in item order in Forge event map.

I see. I thought the metabolic generator would count as a battery because it has an internal capacity of 25, but it doesn't seem to be able to "charge itself" if that makes sense. It needs a battery to charge. I'm surprised that the implants aren't actually prioritized, but the most important ones take "priority" by chance which is nice.

To my understanding, this was the original intended behavior as the non-battery energy source are cleared every tick. They don't store energy per say.
That being said, the energy system implementation is a bit overcomplicated, so I may have missed something in its intended behavior.