I don't think Play Magnus is close to indistinguishable, it's a modified version of Stockfish on the backend, having the same rating doesn't mean you have the same style
Yup. It's absolutely possible to determine whether you play versus a strength reduced/weak engine or a human. Humans make human plans and play according to human best practices, which you can find in chess literature. Engines, however, do not make long term plans and often play very inhuman (perfectly precise, unobvious tactical) moves, that often suprises even on grandmaster level.
I'm not sure if saying engines don't make long term plans is accurate, since we can set them to plan an arbitrary number of moves ahead. I think you mean that they don't have a theory of mind, and thus don't modulate their play based on their opponents.