Phone the dog ranger if uncomfortable approaching your neighbours. My stupid neighbours complained after one day which was because we had workmen in the house (a one off situation) but they were super quick to complain.

Poor puppy must be so lonely. If people can't look after them then don't get one 😡

I would bring it up casually straight away. If it's barking when they aren't home, how else will they know it's happening if no-one tells them? They can't try fix it if they don't know it's an issue. Then I'd give it a few weeks and give them an update as to whether it's got any better.

Be a grown up and have a chat. They probably don't even know.
Calling their dog a mutt is pretty unnecessary, don't be passive aggressive.

If you have told them and the puppy is still barking, ring the council. They can help