why touch id on apple magic keyboard doesn't work with bluetooth while it perfectly works when connected with usb cable? I use iMac silicon 24"

I use iMac 24" M1 (MacOS Ventura 13.4.1) and Apple magic keyboard with Touch ID (wide one). I used this keyboard to replace the small one that came with computer. As long as the new keyboard is connected to iMac via cable Touch ID works flawlessly. However, if I disconnect the cable and keyboard is connected via Bluetooth, Touch ID stops working every time I do this. To restore Touch ID I have to turn the keyboard off and then on and connect the cable. The old keyboard worked well in both Bluetooth and cabled connections