I am sure they would like to, but where does this come from.
This is from our immensely powerful CDC on this subject, starting here at their index.
https://www.cdc.gov/coronavirus/2019-ncov/php/open-america/contact-tracing/index.html
Within that link you will find:
https://www.cdc.gov/coronavirus/2019-ncov/php/principles-contact-tracing.html
Within that are many pdf documents with detail.
The principles-contact-tracing-booklet.pdf is a pretty clear outline.
The download link to that pdf is at the bottom of that page.
Apple and Google (Android) have already introduced apps to support this massive tracking effort in support of the CDC.
Apple in iOS 13.5 introduced an exposure notification API, which lets apps from public health authorities and governments worldwide help people figure out if they’ve been exposed to COVID-19, (to support Contact Tracing).
Android apps are promised as well. I found a link with a good explanation of this app.
https://www.macrumors.com/guide/exposure-notification/