Hello, my name is***** and I have over 20 years of experience as a veterinarian. I'm sorry to hear that your fellow got into his bag of food and ate enough that his abdomen is noticeably larger than usual.
The great news is that he does not seem to be at all distressed by this and is passing stool. He has what is known as food bloat, distention of the gastrointestinal tract due to overeating.
We need to make sure that he takes in enough fluids to keep the food soft and able to move through his gastrointestinal tract rather than getting too dry leading to an impaction. Offer small amount frequently of fresh water, ice cubes to lick, and warmed low salt chicken or beef broth to drink.
We also need to make sure that he isn't overly active which can lead to swallowing air or painful intestinal cramping. Slow walks are fine to keep things moving, but running and overly rambunctious play should not be allowed. If he is overactive that can lead to true bloat (gastric dilatation with or without volvulus or twisting of the stomach axis). Symptoms of true bloat may include restlessness, a tight, rapidly increasing in size abdomen filled with gas, unproductive episodes of attempted vomiting, pacing, panting and sudden death. These pups aren't able to burp, the gas stays in the stomach causing it to stretch and expand quickly.
Bloat is most commonly seen is large, deep chested dogs such as German Shepherds, Rottweilers, Greyhounds Great Danes, and Labrador or Golden Retrievers, but Bassett Hounds can be affected as well.
While it sounds like your pup may be uncomfortable, he doesn't sound like he is experiencing true bloat, he just ate too much.
I would not feed him for a good 24 hours. His stomach should look almost normal before he is fed again. When you do feed him, feed him roughly 1/4 the amount you normally would twice daily. Slowly increase meal size back to normal over the next few days.
You can expect that he will most likely have some diarrhea, but that should clear up on its own over the next 48 to 72 hours.
However if he attempting to vomit but unable to do so, his belly becomes more distended and very tight, or he won't lay down and settle, or he is pawing at his mouth or staggering, then I recommend he see a veterinarian immediately as this can also be a sign of true bloat, which can be life threatening if allowed to progress.
As long as he remains bright and happy, takes in plenty of fluids and is passing stool, and has an appetite when he is finally fed then he should return to normal over the next few days.
Please let me know if you have any further questions.