Do the JGI databases contain genome assemblies which are NOT deposited
on NCBI GenBank?
Yes. JGI is not part of the INSDC so it is not sync with NCBI.
If yes, how can I retrieve them? Both systems seem really redundant to
me doing their own thing for the same purpose.
They don't do the same thing. NCBI is part of INSDC so data deposited there are checked and have to follow specific rules and must contain specific metadata to be sync properly with EBI and DDBJ.
To my mind JGI is a bit more like "dropbox" you deposit your data in a folder and describe it. There is no sanity check about what is really in your file.
I recently discussed with people from JGI, they plan to transfer data they have to INSDC when is possible. And try to minimise redundancy to not hold data that are already in INSDC.
So basically I want to fetch all bacterial genome assemblies which are
ONLY available via JGI / IGM.
Sorry I don't know how to do that. You should probably create a new post for this specific question.