I consider this sarcasm because the way "precious" needs to be understood here isn't traditional.
So, "it" within "it's just precious" here should have referred to the events described within the past sentence normally. But the events described previously were not precious in the traditional sense. Meeting the Queen in person and shaking her hand is a precious moment/event. Graduating from University and walking up the stage to get hooded is a precious moment/event. Being able to witness the first time your child started walking is a precious moment / event. These are traditional uses of the word "precious" to describe things that are worthy of remembering, and valuable in a traditional sense. But it's obvious here that, the events described taken at face value has nothing precious about them. Celebrating someone's pet dying is not a precious moment / event. Wishing that someone's pet died painfully is not a precious moment / event. The moment that A considers themselves moral despite their history is not a precious moment / event. Instead, all these things are ridiculous, hypocritical, and laughable. In that sense, calling these events precious can only be understood by understanding the combination of these events as a joke, and the author's choice of using "it" instead of "these" also reflects that intention that the author wasn't intending "it" to refer to the multiple events within the last sentence, but seeing these events as one single joke. The whole sentence, with the context it was spoken under, is a sarcastic remark. And making the remark in a conscending tone doesn't mean that it wasn't a sarcastic remark. The heart of sarcasm is irony, which is certainly present here.
There are other answers that disagreed with what I described above, and they consider the statement not sarcastic. They argued that "precious" was being used the way it meant per the dictionary, hence it cannot be called sarcasm. But embedding sarcasm within a word is only one way to be sarcastic, it doesn't mean that it's the only way to be sarcastic. It's as if one is attempting to understand a paragraph without considering the context and simply by focusing on words (or one word for our case), which is a grossly narrow way of reading that I cannot agree with. For these reasons, I respectfully disagree with the other opinion provided here.