Should unemployment caused by the government closing non-essential businesses during quarantine be counted as structrural unemployment?
There are lots of different people unemployed, and the answer will be different depending on the person. In your prostitute example, if you left your medical assistant job because prostitution paid more, then it's frictional, because there are lots of medical assistant jobs, but it might take you time to go through the interview process and be onboarded. If you have no marketable skills other than sex work, then it's structural unemployment. If there is another job that you're qualified, but you don't get the job because there are so many other people competing for it, then it's cyclical (which is a bit of a misleading term, since there it's not like there's a "quarantine/no quarantine" cycle, at least not yet, fingers crossed).