Hello @Stephan,
after re-setting everything again and starting over and playing around with it half the night I figured that it has to be the fact, that the bridge is LAN-only.
Now with the newest beta-firmwares installed and reset, it works reliable since about 6 hours to call the API, when the bridge is connected to the internet. When it is LAN-only it stops working properly and gives me all the above headaches.
Could you please revisit the LAN-only behavior of the API and make sure the bridge can work reliable when not connected to the internet?