Thank you very much for your hint. The approach of disabling a thing behind the failed bridge and enabling it again does the trick, at least when I use the OpenHAB API Explorer. Unfortunately, I failed to code the sendHttpPutRequest correctly in a rule. For whatever reason sendHttpPutRequest throws an error although I used the same syntax as in the axample. I will create a separate thread for this issue as the question of this thread has been resolved.
