Your vet is right, tummy problems can result from any other health-problem a bunny has. It’s because illness is stressful and stress impacts the signal substances in the gut. (There is actually a special nervous system in the gut – the enteric nervous system.) The bunny can get a gut slowdown, gas can build up. It can be painful for the bunny. He might not want to eat as much or move around as much as he normally does – that contributes to poop irregularites. Antibiotics kill off good gut bacteria, that also effects poop size and amount.
It’s great that he’s eating and drinking water. Water helps hydrate the intestinal contents. A bunny in gut stasis looses its appetite.
Small poop is an observandum, so keep a close eye. There are bunny probiotics you can give during or immediately after a course of antibiotics to help restore gut microbiota. If he shows signs of gas (also generally manifests itself as refusal to eat), you can give baby gas drops (simethicone).
Normally we recommend wet greens for “pepper-corn” poop – but this is obviously not the right time to introduce any new food.