I didn’t find it in Aurora Store for some reason,
The reason being: it’s reported as not compatible with your phone because it’s not matching some of its requirement (usually stuff like OS API version, etc.). In your case, that is …
I believe the missing piece here is the Android emulation layer which has extremely limited support for Bluetooth (speakers only IIRC).
Contact tracing require direct access to the bluetooth hardware (so that the Google, Apple or in your case microG service can send the random ID, and detect other people’s random ID and make that available to your local app).
But, indeed, the AlienDalvik layer used in Sailfish OS doesn’t give this access (because the underlaying Linux uses BlueZ like any standard GNU/Linux distribution, whereas Andoird uses it’s own thing, and there’s currently no translation layer between the two APIs in Aliendalvik. Thus Android apps are limited to only devices that are handled on the Sailfish OS side of things and appear as standard devices inside AlienDalvik: bluetooth speaker (appear as simple audio output to android apps), bluetooth keyboards (appear as standard input to android apps), etc.)
From the point of view of Android Apps, your smartphone doesn’t have any bluetooth, only a bunch of standard devices. That’s why the contact tracing app doesn’t show up in either Aurora or the official Play Store.
The must necessarily be handled in a Sailfish OS Native app.