Just looked at https://healthdata.gov/Hospital/COVID-19-Reported-Patient-Impact-and-Hospital-Capa/g62h-syeh for my home state.
While nosocomial COVID isn't reported in such a way that you could count the total cases, I can calculate that between June 1 and June 17 (latest available date), the proportion of hospitalized COVID patients who *must* have been infected SARS-CoV-2 after they were already in the hospital for something else (because they tested positive more than 14 days after they were admitted) rose as high as 9.3%, and never dropped below 4.9%.