While removing the brake assignments from the devices, I found a solution. In Spadnext, I had one assigned to the throttle button (the button you click while moving the throttle – throttle position). It was assigned to autothrottle disconnect. This caused A/THR to be disabled with master caution when landing and moving the throttle to idle, which likely affected the BTV shutdown. After removing this assignment, everything is fine now. Sorry for the confusion, but I wouldn't have guessed I had such an assignment in my Spadnext profile.
Wiggle's post in Automatic turning off of the BTV after moving the rudders. was marked as the answer