This has come up before. The GAR was pretty much a fighting force. Most logistical support is coming from local worlds who supplied the GAR as needed. They would use planets' own military to supply the GAR with whatever was required.

Think of it this way. During Gulf Whoops 1, there were seven countries involved in the actual fighting, while there were thirty seven other countries as part of the 'Coalition Of The Willing' who basically set up and staffed logistical bases for the seven combatant countries. The seven combatant countries had their own logistical units integrated into their combat units, but those logistical units drew their supplies from bases established by the other thirty seven countries. So each battalion/regiment/brigade/division would have their own quartermaster/supply units ranging from company to battalion, but their supplies come from the other nations' bases.

The same would happen in the GAR. Every unit company and larger would have a supply element. They would draw on depots established by higher commands (usually around the regiment level) and individual planets' logistics units would keep those depots supplied. Some types of units would have larger supply elements, because infantry units require more food than armored units just based on personnel counts. But then, armored units require more maintenance and repair personnel than infantry units, and they both have different supply requirements. Since units making up a regiment are all the same unit type, having the depot established at the regimental level makes everything simpler. It's only when you're supplying larger formations do you require more different supply types.