Yes, you are correct - if the underlying descriptor supports notifications, the connection should be successful (a notification "Notifications for characteristic enabled" should be displayed and GUI-O should show "Connected" status).
Yes, "Connected device not responding" means that GUI-O application received no data (which was expected in a certain time interval after pressing the initialization button).
Firstly, you can try enabling local logging under the Developer mode menu. Navigate to Info menu and press Application version 10 times. A new menu entry should appear at the bottom (Developer mode). Please enable log incoming and log outgoing messages.
Retry your setup and exit the GUI-O app. Use a file manager to navigate to Android/data/com.guio.guioapp/files and check in_messages and out_messages logs. Is there any data there?
Note that for Android 11 you will probably need a PC to access this directory (due to Android restrictions).
Next, you could also try ignoring the initialize button and send the data from your device to the GUI-O application after successful connection (you don't need to trigger the @init command, GUI-O can still receive data).
I will try to check with my Bluetooth LE module tomorrow and will report back.