In this case systems are the S of ECS and contain all your game logic, acting upon the entities and components (E and C).
By system management I assume they mean the APIs bevy offers for scheduling and sequencing systems and events so your game logic remains modularized while still running in the correct order.
Exactly this.
It seems like you're calling an entire game engine "ECS". I'm not sure what the point is here, the whole question was what justifies having a 50 MB hello world binary. It doesn't matter what you put into a data structure, the data structure itself shouldn't make 50 MB binaries.