The product page (https://www.punkt.ch/products/mc03-premium-secure-smartphone, click on "all tech specs") mentions a "SAR sensor". I have not seen that before, does anyone know what this does? Does the device try to estimate how much EM your body received while carrying it around or calling, or what is this for?

Yep, SAR stands for "specific absorption rate". These sensors are typically used to change how the antennas on the phone transmit (like how much power they use) by detecting whether the phone is held close to your body vs. sitting somewhere like on a table.

Most phones have them.