The problem with this question is that it asks for comparisons to a "canonical Chinese mythology" which is not really a thing. However, the basic theme of traditional Chinese folklore does feature an emperor in heaven who is essentially a mirror of the emperor on Earth. The depiction of the Jade Emperor in Journey to the West matches much of this.
1. Slackers are punished severely.
We see this in, for example, the tragic love story of the Weaver and the Cowherd. An ancient version of this story, recorded in around 6th century, says:
On the east bank of the Celestial River, there is a weaver. She is the child of the Celestial Emperor. Year after year she toiled to weave celestial garments, looking busy and disheveled. The Emperor felt sorry for her loneliness, so he married her to the Cowherd from the west bank of the river. She stopped weaving after the wedding. The Emperor was enraged, and punished them by making them return to east and west separately. But he had them meet once per year.
Here we see the Celestial Emperor reacting to her daughter
going on honeymoon slacking off with inhumane harshness. This is despite the marriage being his own idea and all her previous years of hard work. I would also argue this demonstrates inflexibility and a quickness to anger on the Emperor's part, just as you saw in the novel's version.
2. The powers of the Jade Emperor is purely authority
The Jade Emperor is essentially the administrator of the heavenly court. Just as the Chinese would not expect the temporal emperor to personally arrest vandalising teenagers, the Jade Emperor metes out punishment and rewards not by doing any work himself, but by exercising his authority as the ruler of heaven.
An example is the story of Lightening.
Once upon a time, Thunder worked alone, striking down people who were wasteful from the clouds. Back then, an impoverished but pious woman struggles to provide her mother-in-law with the best. To save on costs, the woman serves the mother white rice, then retreats to the kitchen to eat only bran herself. The mother however suspected the pious woman of keeping the good food for herself.
So one day, she barged in to see for herself what the daughter has been eating. Discovering that the daughter-in-law has been eating bran, the mother was heartbroken. She told the daughter to dump the bran and come eat the good rice with her. Unfortunately, it was a stormy night and Thunder was patrolling. Upon seeing the pious daughter throwing the bran away, he struck her down, thinking she was wasting perfectly good food.
When the Celestial Court heard of this miscarriage of justice, the Emperor was filled with great sympathy. To reward the daughter for her piety, he ennobled her in heaven as Lady Lightening. To prevent another tragedy like hers from happening, Lightening accompanies Thunder out on patrols, and illuminates the earth before the thunder strikes.
That's why thunders are always preceded by lightening.
There are many variations to this story, but the ending is essentially identical: the Jade Emperor gives a victim "justice" by using his authority as administrator of the Celestial Court to give her a job in Heaven. Not to raise her from the dead, or give her family a fortune, or do anything really that involves using any sort of divine power. Instead, he issued a decree.
3. The Jade Emperor is short-tempered.
The Chinese have an ancient saying:
伴君如伴虎, literally, accompanying the ruler is like keeping a tiger company. Chinese Emperors were notorious for being ill-tempered with little regard for just about anyone else. Since social interactions in the Celestial Realm were imagined based on realities, the Jade Emperor seems to have inherited such traits.
An illustration of these traits in folklore is the legend that the Immortal Poet Li Bai was the Great White Golden Star in heaven.
The Great White Golden Star works as an alchemist in heaven. Being an alcoholic, he got drunk one day and accidentally knocked over an alchemy pot. The Jade Emperor was enraged, and stripped him of his godhood, sending him to be reborn on earth as the poet Li Bai.
Somewhat of an overreaction.