How many of you folks agree with me that the admiral should have accepted Osyrra's offer?
It was a good offer, by the Admiral's own assessment. She was willing to accommodate further demands, including her own resignation. But asking her to face trial, presumably under retroactively applied Federation law, was not reasonable, and she could not possibly accept. Her offer, and the risks she took to be in a position to make it, were already acts of extraordinary desperation. But the admiral's decision made it clear that only by completely destroying the federation could she possibly survive. This made it inevitable that many more people would suffer and die (including, as it turned out, the crew of the giant ship that took Discovery inside - not just Emerald Chain military, but slaves and servants too).
She was no angel, and had given many people and peoples cause to hate her. But no one who has been in charge of any large government for any length of time has been particularly good, to the best of my knowledge. If they don't create terrible, awful and evil policies of their own, they continue them. If she was in fact unusually awful by the standards of her own people, they might have brought her to justice in the end. We have no reason to think hat her proposed armistice included federation protection from such justice - she only agreed to resign after the admiral implied it might be necessary.
I considered the possibility that he saw her as a threat to his own position. It is obvious that the general is something close to a dictator in his own right. We've never seen the rest of the federation government, and few democratic governments would have given him carte blanche to negotiate a settlement. But once she agreed to resign, she was no threat to his position. So it makes no sense from that perspective either.
His action was not consistent with federation history. They made peace with many peoples who had done bad things without requiring such terms of vengeance.
When any major government falls apart, the people possessing advanced scientific and engineering knowledge, as well as those controlling the advanced technologies and weapons systems, sell their skills, knowledge, and systems to whomever they can. (E.g., Nazi Germany. The Soviet government. Etc.) That creates all kinds of chaos. Osyrra's offer made it possible for the federation to buy these people's knowledge, science, and take control of these technologies and weapons systems, in an orderly fashion. It was the right choice.
I don't know how much of that chaos the show will present. But in the real world (or, since this is Star Trek, worlds), it would happen.