Hi,
I did not read the previous replies yet but I got the problem on one more device - a brand new Poco M5s. Unboxed device, Android 12 + Miui 13.0.1.0 was there. Installed KSK (restored apps from old mobile via Google cloud account backup - not physically copying from old device - KSK automatically installed by Google, but I doubt any app settings was transferred). No overlay icon yet. Updated device to Miui 13.0.3.0 (2x security patch) and after device restart (and without starting KSK manually), the troubling KSK icon appeared!!! KSK has still no account configured, still clean install!