Tried a real Android 12 (S) install from scratch today … wiped system, wiped data before … same issue.
Tried to install the prior microG build with Exposure Notifications via adb install -d … same issue.
Installed 1.5-r-20221030230467-dev-FP3 from scratch … issue is gone, microG with Exposure Notifications works after installing it. And Lawnchair 12.1 installs and works just fine, too (I missed checking that again with the new Android 12 install).
I’m staying with Android 11 (R) now for a while, it seems.