@mautz
Seemingly the kernel I compiled doesn't support the BT sleep mode. (There is no '/proc/Bluetooth/sleep'. Well, there is no /proc/Bluetooth at all and I just checked and the Bluetooth cannot be turned on.)
Could you let me know what flags needs to switched on the in the defconfig to get this working, please? Thank you.

Edit:
I have found them :

CONFIG_BT_HCIUART=y
CONFIG_BT_HCIUART_H4=y

Edit2: ...and both of them are in my kernel config.