(Disclosure: I work for Google)
(Disclaimer: I work on an app that tries to do that. Ideally privacy preserving. And we implemented it using Google Nearby API to detect whether people are close. But that sends all messages over Google servers and that would be a deal breaker for us, but the tech itself would be really cool to have. Let me know if you can help.)
Also Related Work:
Singapore doing this: https://www.tracetogether.gov.sg/
This as hardware: https://estimote.com/wearable/
You could have something where people who have it can say "I have it, please let others I was near know" but unless we get testing up dramatically that won't work either.
Also, the alternative of total lock down is hard to beat when it comes to false positives. ;)
And how would you find a list of such questions without just broadly matching on terms like "coronavirus"? The task seems very complex to me.
It almost feels like breaking some higher contract with society by reserving that power for advertising and not using it to tackle the pandemic.