The whole reason behind the poisoning of Saskia was for Stennis to secure the position on the throne. The trial probably followed the same format, clearing Stennis due to a lack of evidence.
In the quest, there is not much evidence that can directly prove Stennis was involved despite what is suspected. The exact details of the trial were not shown, but he was presumably cleared. Geralt speaks about his suspicion, calling Stennis a “poisoner” but the rationale behind letting him live was because despite Stennis’ crimes, a mob lynching was not what Saskia would have considered to be justice. If you let Stennis live, the game will tell you he poisoned Saskia.
