I totally agree with you that an unofficial warning would have been best. Her coach made his admission after the match, not during, so it wasn’t provable during play - it was simply assuming Serena was seeing the gestures. Her coach also also said that the other coach was making hand gestures the entire match too - he said all coaches make gestures.
The point is that the Umpire cannot definitively prove that Serena saw the gestures - the coach is sitting behind others which blocked the view based on the positioning of seats, so it’s debatable if the player can see anything and Serena has said she didn’t cheat, whereas the chair Umpire is in an elevated position making it easier for him to see spectators behind others. For all the umpire knew, or could prove, her coach could have just been explaining strategy to the people next to him - essentially reasonable doubt. A warning to Serena would have allowed her to tell her coach to stop whatever he was doing without assigning blame