It was probably hard for Discovery to have a clearly defined chief engineer without having a clearly defined engine room.
The engine room was clearly defined..
To my memory, we never actually saw Main Engineering. What we saw throughout the series was an engineering lab, or something to that effect.
This is the engine room, with the warp core, of the Discovery:
It's ridiculously large
For scale: These are people in the red box.
The warp core ejection tube:
They are, supposed to be, between the shuttle bay and the hull.
Non of this fits inside the secondary hull of the Discovery.