I was having the same issue. But it was 2yr old. Just random 4 inch holes all around the backyard. Not the common long shallow digging they do to lay in cool dirt. My backyard was a mine field of tripping hazards. I did put poop in the holes, and those holes were left alone. The ones I didn’t put poop in were dug up again.
What finally stopped the digging? Constantly being out with him (thank god for the mobility chair!) and corrected him with a verbal “attt” when he would start. I also gave him an area he could dig in, and he doesn’t seem all that interested anymore and dug there maybe once or twice. But I also started giving him jobs outside, but I think your pup is too young for that yet. We’d put his backpack on him with weights, or let him pull his sled around with weights.
He typically goes back to digging if he isn’t worked enough, so I’m not sure about it working on a pup, but could t hurt to try! My pups don’t dig.
I don’t know about the mulch, we have heavy river rock. The dogs would race through it chasing each other and knock the rocks out, and then we had a mine field of rocks and holes. We just fenced off that area (which also has access to the pool) and now no more holes or rocks everywhere. And the grass is finally starting to come back in too. That was a combo of upping mental/physical stimulation, constant watching when he was outside with verbal corrections, and the fence, but the fence was just so they couldn’t go swimming whenever they wanted to.