Why did the budget move to the ad set when I increased a CBO campaign at its cap?

When the engine (or a manual increase) asks for more budget on a CBO campaign that has already reached the campaign budget cap, the new amount is written to the ad set, not the campaign: Meta limits the campaign budget and accepts the adjustment at the ad set level.

The CBO history also records the value Meta actually wrote, not the value requested: what you see in the history is what is in effect.