Thank you for your fast answer, it really help me solving the problem.
First I implemented all your recommendations in app inventor application. That did not change anything to the problem but I will keep them in my final app as "best practices".
Next, I thought about your comment on the MTU size. On the ESP32 code, I changed the "advertizing" long name (19 ascii bytes) to fairly short name (3 char). Connection is now successfull both on the small Arduino IDE demo app as well as my quite larger app. So far so good since I get a working environment, nevertheless I would like to use larger name, and will try negotiating larger MTU size.
The way I plan to use BLE is to exchange strings between client and server (sending quieries from client and receiving corresponding replies, sending configuration parameters ) and also sending integers (values read from peripherals like temperature an humidity sensor) from server.
again big thanks for your detailed answer.