Is it possible to use a Smartphone audio jack as MIDI output?
No, you can't use headset audio output for MIDI output.
The TRS connector on smartphone is meant to be connected to headsets, it has no circuitry that is compatible with MIDI.
MIDI interface is an opto-isolated 5mA current loop, and currently it is allowed to be used with 5V and 3.3V supply voltages. Traditionally a 5-pin DIN connector is used, but these days also a TSR connector can be used for the same signals as devices have gotten smaller and portable.
So even if some devices use the same TSR connector for MIDI than what smartphones use for headsets, it does not make the devices compatible just because they use the same connector.
The Arturia BeatStep uses a standard MIDI output interface, but with a 3.5mm TRS connector, and thus it needs an adapter to provide a MIDI output with a standard DIN connector. The 3.5mm TRS port on the Arturia BeatStep is still a MIDI port, while the 3.5mm TRS port on smartphone is still a headset port.