Which was another massive downside for the Volksturm. Nobody had a clue what ammo to send to who so once their initial issue was gone they were screwed.
Whereas the Home Guard were all armed with weapons which fired standard British ammunition (eventually).
That certainly was a logistic challenge but I don't think so much in the Volkssturm. The Volkssturm units were not intended for a campaign where the troops moved forward or backwards and had to be continuously supplied, but were supposed to take the one and only battle in its home region with what it had - game over - win or die. I doubt if there was any resupply schemes or capacity at all.
In that context I think issuing the Volkssturm with the countless weapons and ammo taken in various occupied countries like it was optimal to place confiscated artillery in static positions in the Atlantic wall. A lot of field army units also were equipped with foreign materiel, but some of that wasn't more foreign than still being produced in German controlled factories. The Pz 38 is one example, but AFAIK a lot of French trucks and spare parts were produced in occupied France and delivered to the Wehrmacht.
Next we often tend to evaluate German logistics by US Army standards. Apart from US doctrine requiring much more arty ammo (about 75% of the logistic burden) the US system meant each part being transported first over an ocean and then continuously distributed to the engaged units. That was extremely complicated and required the number of different parts to be managed to kept as low as possible. The German system was very different, not just because of the much shorter lines of supply, but mainly because German army units were not expected to be kept up to strength during an engagement, but basically fought until having spent its combat power and then either ceased to exist or was withdrawn to be rebuilt - with new men, materiel and ammo supply. So, in the German logistic system you didn't have to keep track each day all the way to the frontline of "that kind of oil filters for that Divisions and that kind of tires for that Divisions" but when a Division was withdrawn for rebuildling they got what was stockpiled near them and spent it in the next engagement - simply put.
Of course they preferred standardised materiel, all other things being equal that is an advantage, but the German system made it possible to utilise a lot of materiel that otherwise would have been wasted and so was specialised for the German situation. They wouldn't have benefitted from the US system and the US wouldn't have been served with the German.