It turns out that the fabric seat cover, and/or the gas suspension creates such a strong electrostatic discharge (ESD) that my screen shuts off for a short time.
The solution? No idea yet, but it seems that insulating the chair with copper foil and connecting it to a socket (ground) might help, as you can see here:
Welcome to 2023 - Your Ikea "MARKUS" chair is not compatible with your screen 👏🤦♂️