Garages just use a flexible hose something like dryer vent to route exhaust gases outside in case they have to run an engine inside the shop space.

How hard would it be to partition a space for the genset off and ventilate that area. Basically a generator room.

Most of our industrial gensets (caterpillar units) at mines and construction camps were in very simple sheds that were little more than a roof and only protected against rain and snow. We didn't even sheath the walls all the way to the ground so the shed was well ventilated.
We expected diesel units to start automatically at -40 so they did have block heaters and fuel preheaters on them.
(I doubt if you will need that)

Maybe you could add some louver vents to your shed in the generator's room. Both low and high to get rid of heavy and light gases.

Fuel storage is always a problem. If you can't leave it out in a little dog house of its own then in the outside shed where you intend to put the genset is the next best thing.
The farther from where you sleep the better, (right?)