Ah, I figured it out – apparently ‘tobii_config’ does write the calibration under ‘~/.config/Tobii Config/’ but it takes auxiliary ‘tobii_engine’ service to publish it for the clients. The latter is marked as merely ‘recommended’ in the Stream Engine online documentation and corresponding client API appears to be stripped from the latest Linux release so I never bothered to adapt its Debian package for my system until now.
I can confirm the screen calibration persists across hardware power cycles as long as ‘tobii_engine’ service is operational.