Well, Support gave up, they can’t help and won’t try with a debug version to see what is wrong.
I tried with Revo Uninstaller and deleted all keys and files, reinstalled, and it’s still the same, empty game list…
I checked with Process Monitor and could see it still scans for Steam games by reading some appmanifest files, so it knows where and what to scan, but it just won’t show anything and not work at all in supported games that worked before.
So I’m stuck with no Tobii support in Elite Dangerous unless the devs decide to support it natively.
And as it was the only game where I used it (because FS 2020 does not support it either), I’m left with a useless Tobii device now.