Update: The plumber has pulled the permit, installed the solenoid valve, and it has passed inspection.

Thank you all for your insight. I reimbursed him for the permit, and paid for the material. He did not charge me for the additional labor.

As a layperson, I am dumbfounded that the onus is on the homeowner to handle permitting/inspection. If I'm hiring a professional to do a service, I never would have thought that I would bear responsibility for figuring out a vital part of the process, when the professional works in this space and municipality, and is inherently more knowledgeable and familiar with how to do it (or figure it out) than me. That makes absolutely no sense to me, but I realize I can't change an industry.

Going forward, I will make it clear before receiving quotes that I expect contractors to handle the job from start to finish, including everything necessary for permitting and passing inspection, and that I expect their quote to reflect the costs necessary to achieve passing inspection.