I use zwift play and a tacx flux. I have noticed when I change gear the brake light shows up and my bike slows down. Today I did a slow gear change to avoid the chain falling off and my bike came to a stop.
Probably worth adding an image of your handbars as i can only assume you are catching the play paddles and pushing them in wards causing it to brake.
is it possible to attach them a bit lower maybe?
Most likely the shifter is enganing with the orange paddle with out you realising it. Small adjust to the position of the play units should resolve this