Hi Juanito,
(1) The script- bt_start.sh works properly on RPi-400 running PiCore64. Thanks for sharing the same.
(2) However, the script does not work on the same device while running on Picore-13.0.3. It throws up an error of being unable to load the bluetooth module (modprobe: can't load bluetooth (kernel.tclocal/net/bluetooth/bluetooth.ko) : unknown symbol in module, or unknown parameter)
P.S- On PiCore64, after running the script, I was able to connect the RPi-400 to a bluetooth speaker. But unable to test audio ouput on the paired device as I was not getting any audio output in the RPi-400. While trying to play a video on Firefox, pavucontrol was relaying sound to "Dummy output". I am trying to fix the same (read suggestions of setting hdmi_drive = 2 in config.txt). So, I will update after testing audio output on the paired Bluetooth device.
Strangely, while running Picore-13.0.3, I was able to get audio output on the same RPi-400 device through attached speakers on a Samsung TV monitor connected using HDMI. The same setup was not giving audio output with PiCore64. I wonder why..