The Dragon Project by Naomi Kritzer

The Dragon Project by Naomi Kritzer (Clarkesworld #186, March 2022) begins with the narrator, a bioengineer, getting a commission from a client to make a dragon for Chinese New Year:

People had been asking for dragons for a while, but this client—I think he was a hedge fund manager who was starting a new entertainment streaming service, but possibly he was an entertainment streaming service CEO who was starting a hedge fund. Did I mention I’m bad at paying attention in meetings?

The first dragon was about the size of a cat, and since the client had refused delivery, I kept him. I fed him crickets and mealworms, shaved carrots and diced peppers, crunchy cat kibble, and occasional cans of sardines. The dragon grew plump, developed a habit of begging at the table, and shredded my sofa and curtains with his claws. He also liked to lie across the back of my shoulders when I was working, like a tiny scaly heating pad. (Despite the scales, he wasn’t a reptile; I had thought a warm-blooded dragon would have a more interesting personality. There are scaled mammals, like pangolins.) He ran around the house with a little galumphing hop.

After the first dragon is rejected by the client—no wings, no fire, wrong colour, wrong size, etc.—she starts work on a second dragon. This one—larger, with feathers, teeth (although still no fire due to potential insurance problems)—is also rejected. After this, her business partner fires the client. The partner takes the second dragon home while the narrator keeps the first, which she names Mr Long.
Time passes. The dragons prove popular when each of them is out and about, which leads to further work for her and her partner’s company.
The last part of the story (spoiler) has the narrator hear of a fire at the CEO’s company: she realises that he must have found someone to create a fire breathing dragon for him. Then, sometime later, when she hears rumours of a strange creature in the wild (“the Palo Alto Hippogriff”), she realises that she had better go and find it (fire breathing dragons and dry Californian forests are not a good mix). With the help of her dragon she does so. Minor problems with their ex-client ensue.
This has a slight story line, but it is an entertainingly told piece.
*** (Good). 3,850 words. Story link.