Distributed docs are a bit contradictory as to if it loads packages you are `using` on the manager process

The answer is:
Yes it loads them (requires them, i.e. don't bring into scope), on all workers, when you using them on the manager,
but when you start a new worker, it doesn't start with the ones that are currently loaded on the manager process.

https://docs.julialang.org/en/v1/manual/parallel-computing/#code-availability-1
first says:

Finally, if DummyModule.jl is not a standalone file but a package, then using DummyModule will load DummyModule.jl on all processes, but only bring it into scope on the process where using was called.

Then later kind of contradicts that:

Note that workers do not run a ~/.julia/config/startup.jl startup script, nor do they synchronize their global state (such as global variables, new method definitions, and loaded modules) with any of the other running processes.

The second bit is kind wrong.
It does synconize loaded modules.

Read the distributed-computing manual section at the linked URL, especially the statements about using packages and synchronizing loaded modules. Reconcile the wording so it accurately distinguishes modules loaded on existing workers from the state of newly started workers; the documentation is done when those statements are no longer contradictory.