Maybe it was more of an unexplained 'helpful sidekick' kind of thing, like Wolfea helping Will. It definitely wasn't explained thoroughly enough though.
I never thought the pets were like Patronus in Harry Potter...but more like the actual pets in Harry Potter...you know, every child either took an owl, or cat, or rat, to school with them. Those pets did not have major roles in every book, but they did come into the plot here and there. I certainly don't think this book is anything like Harry Potter. However, most books for kids are going to have animals in them because having pets is something kids can all relate to. They may not know what it is like for Will to experience having a missing sister or being thrown into a different world. But they do understand how they would feel if someone hurt their dog. The pets make the story relatable. And yes, I agree that they should have been used more in the plotline and been given their own heroic moments.
I think including the act of giving pets to the kids was meant to show nature's beautiful form of compensation. The fact that the kids stayed in an orphanage did not imply that they were outcasts and that they could still find comfort with what was readily available. Wolfea's featuring in the book was also critical in the sense that it advanced Will's altruistic qualities because on would expect him to only focus on saving Emily.
I know that the pairing of the children and pets in this book was unexplained but I feel that maybe it was to give them some sense of responsibility and companionship