Doesn't matter. https://content.sciendo.com/view/journals/popets/2019/3/arti... - note that this is seemingly aptly published in a conference on privacy. Yes, what you want to use bluetooth for would likely work but we've worked a decade or so to prevent it.
You'll likely realize from my other comment that I dislike the general idea of this but honestly, I don't get the approach from a technical perspective. The idea is an app for smartphones, right? You have all kinds of sensors on those besides BT, e.g. WiFi, GPS. Comparing timestamped movement profiles would give you much better matching than approximating this stuff via BT environments, which these days at least theoretically are designed to explicitly prevent your use case and just seem to limit yourself artificially. The reason you dismissed geolocation is perfectly valid but that also applies to Bluetooth identifiers if you treat them as reliable indicators. If I get a (hashed or not) BT ID of infected persons, I can identify those - at the very least if their device is in my vicinity. And not only while this issue is active but afterwards. You would have to protect that data just as much, putting another ding in the "potential privacy implications" of the approach.