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This drove me nuts and it was very difficult to find a solution, so I'm sharing it here in case it helps anyone. Credit goes to Tamantha on Steam.

The trick is that when you're playing as Latha/Mandala and controlling the service drone, you mustn't click the Close button in the top right to back out of the camera view. Just directly switch to a different character and place the grenade on the drone. Otherwise, the drone gets lost in the machinery without the grenade going off.
I don't recall if this was an issue when trying to do things by the book, but it was definitely a reproducible problem when going for the gruesome ending.