My hospital, for example, requires COVID testing right before any elective surgery (for example, a hernia or knee tendon repair - I know well, having had a patellar tendon repair in January 2022). We know who has been vaccinated and who has not. Relatively easy calculation, albeit with a non-randomly selected population. Remarkably in the USA, the vaccination rate is not especially small (33 percent of Americans are not cully vaccinated).

Michael