That one is obvious due to us knowing the hospitals sell to the government and insurers for much less.

As far as I am aware, this does not apply to a veterinary business. The article also says it was $10k for emergency services at a vet hospital, including the aftercare.

What are the labor costs of having highly qualified people, presumably in low supply, on call to provide these services? What are the costs of supplies like medicine, and malpractice insurance (if that applies)?

The vets that I've been too (minus a non-profit clinic I went to once) absolutely charge outrageous amounts for saline and other things. It's a hard business, so like most time-of-use sales points they take advantage and charge for the convenience. I'm not making a value judgment, just pointing out that it definitely is something they do.

What is definitely something they do? Asking for higher prices in high demand low supply scenarios? That is something (effectively) everyone does.

It is how the world works. It is the mechanism which the markets use to signal more supply of something is needed (or less demand).

If you want me to study advanced biology for 10+ years and then have me work at odd hours of the day and night to be ready to perform surgery, you need to pay up, or reduce the other options I have for earning money which give me a higher quality of life.

Again, I'm not making a value judgment (as rationalizations from both perspectives can be made, and a person's opinion will depend on their perspective), just saying that "charg[ing] outrageous amounts for saline and other things" is definitely something they do. In a free market system they're allowed to charge whatever they want, and the consumer is allowed to take it or leave it. But explicitly stating the practice is a fair thing to do.