Did not read the paper so apologies if this is covered but isn't it possible that there is some recognizable semantic pattern in the training data where an "aha" is often followed by a subtle semantic shift that proves closer to the original premise in some critical way, and by emitting the "aha" token the model causes itself to produce such a subtle semantic shift that pushes the subsequent reasoning closer to the desired response?

It amounts to noise overall, but it has further unwanted and potentially misleading 'properties'. I think it's rather sobering to see how much bandwidth is still being wasted.