Khan was from the 1990s. La'an was born in, what, the 2230s?

Assuming the augmentation dilutes with generations of intermixing with normal humans, I'd presume that by the time La'an comes around that she has so little difference from baseline human DNA that Starfleet doesn't care.

It's a judgment call, and I suppose that you can't put an exact line on when the augmentation is diluted enough, but in the eyes of Starfleet she is clearly past it. The spirit of the anti-augmentation laws are prevent new augments, which is supposed to prevent a case of some kind of augment takeover. La'an having a distant family line to augments doesn't seem to pose any kind of risk like that.

Una was straight up an augment. Her DNA was directly tinkered with before birth. That's exactly was Starfleet, or more precisely humanity is fearful of.

I don't think we can really look for some kind of codified judicial procedure for a situation like this. The anti-augment laws exist out of fear, and that balances against the more enlightened nature of humanity in the future. Simply, people in charge are afraid of what is Una in a way they aren't of La'an.