It's never made much sense that the entire multi-species Federation would be subject to a strict ban on genetic engineering due to events on Earth that happened centuries before the Federation was even founded. The way they doubled down on that rationale in Una's trial only highlighted the absurdity -- especially when Admiral April claimed he would exclude Una to prevent genocide.
On the one hand, the writers may be trying to create a straw man out of a weird part of Star Trek lore so they can have a civil rights issue in Starfleet. And that's fine. From an in-universe perspective, though, I think we can discern another reason for the ban on genetic engineering -- the Klingon Augment Virus.
There was a ban on genetic engineering on United Earth, which is understandable given that it was much closer to the time of the Eugenics Wars. Why would that remain unchanged when more time passed, more species joined, and more humans lived in places without living reminders of the war? [NOTE: I have updated the paragraph up to this point to reflect @Value Subtracted's correction in comments.] The answer is presumably that they needed to reassure the Klingons that something like the Augment Virus would never happen again. Hence they instituted a blanket ban around that time -- perhaps in 2155, the year after the Klingon Augment Virus crisis and also, according to Michael Burnham, the year the Geneva Protocols on Biological Weapons were updated.
That bought the Federation over a century of peace, but after war broke out due to a paranoid faction of Klingons who thought humans would dilute Klingon purity and after peace was only secured through the most improbable means, they doubled down on the ban. Una's revelation provided a perfect opportunity to signal to the Klingons that they were serious about the ban -- hence why they would add the charges of sedition, perhaps. Ultimately, an infinitely long speech and the prospect of losing one of their best captains combined to make them find a loophole -- but not to invalidate the ban or call it into question. This Klingon context is why April, who we know is caught up in war planning of various kinds, is so passionate that the ban exists "to prevent genocide" -- he's not thinking of people like Una, he's thinking of the near-genocide they suffered at the hands of the Klingons.
This theory still doesn't paint the Federation in a positive light, since they have effectively invented a false propaganda story to defend a policy that has led to demonstrable harm. But it makes a little more sense, at least to me. What do you think?
If the purpose of prosecuting Una was to signal the Federation’s seriousness about a genetic ban to appease the Klingons, then why offer a plea deal with a sweetheart sentence? Why keep the records sealed? Why even bother with not charging her with sedition initially?
No, this isn’t plausible to me. If it was a show trial for a diplomatic purpose, it’d be full on from the beginning, no deals and having a Klingon observer in the courtroom. There’s no need to be coy about it.
It’s obvious that Starfleet and the Federation is embarrassed at having had an Illyrian not just join, but climb the ranks to be the best first officer in the fleet. That’s reason to sweep it under the rug, not use it as a message for the Klingons.
According to Worf the Augment virus and its effects are “not something the Klingons discuss with outsiders”. This show trial was about appeasing the High Council and assuring them there wouldn’t be more augmented officers after Una; not about appeasing the Klingon people. Observers etc would have been too high profile.
I missed the Klingon observer? Where were they?
There wasn't one -- that's what @khaosworks was pointing out.
Okay, first they try to cover it up, because it's easier if the Klingons never find out. But then once she's uncooperative, you go all out to show it's serious. And you don't have a Klingon observer because you don't want the general public to know the Klingons are dictating such an important domestic policy.