Ok, after fresh module build when updating my Mint laptop to kernel 6.5.0-27-generic the keyboard is working again.
So now I'm sure the keyboard itself is working.
Details of bluez version installed on my laptop:
erik@laptop-erik:~$ sudo apt list | grep -i bluez
bluez-alsa-utils/jammy 3.0.0-2 amd64
bluez-btsco/jammy 1:0.50-0ubuntu7 amd64
bluez-cups/jammy-updates,jammy-security,now 5.64-0ubuntu1.1 amd64 [installed]
bluez-firmware/jammy,jammy 1.2-7 all
bluez-hcidump/jammy-updates,jammy-security 5.64-0ubuntu1.1 amd64
bluez-hcidump/jammy-updates,jammy-security 5.64-0ubuntu1.1 i386
bluez-meshd/jammy-updates,jammy-security 5.64-0ubuntu1.1 amd64
bluez-meshd/jammy-updates,jammy-security 5.64-0ubuntu1.1 i386
bluez-obexd/jammy-updates,jammy-security,now 5.64-0ubuntu1.1 amd64 [installed]
bluez-obexd/jammy-updates,jammy-security 5.64-0ubuntu1.1 i386
bluez-tests/jammy-updates,jammy-security 5.64-0ubuntu1.1 amd64
bluez-tests/jammy-updates,jammy-security 5.64-0ubuntu1.1 i386
bluez-tools/jammy 2.0~20170911.0.7cb788c-4 amd64
bluez/jammy-updates,jammy-security,now 5.64-0ubuntu1.1 amd64 [installed]
bluez/jammy-updates,jammy-security 5.64-0ubuntu1.1 i386
libasound2-plugin-bluez/jammy 3.0.0-2 amd64
libkf5bluezqt-data/jammy,jammy 5.92.0-0ubuntu1 all
libkf5bluezqt-dev/jammy 5.92.0-0ubuntu1 amd64
libkf5bluezqt-doc/jammy,jammy 5.92.0-0ubuntu1 all
libkf5bluezqt6/jammy 5.92.0-0ubuntu1 amd64
python3-bluez/jammy 0.23-4build1 amd64
qml-module-org-kde-bluezqt/jammy 5.92.0-0ubuntu1 amd64
erik@laptop-erik:~$
Display More
Address: 00:1F:20:04:44:38
Address type: public
Name: Logitech diNovo Edge
Alias: Logitech diNovo Edge
Class: 0x002540
Appearance: 0x0000
Icon: input-keyboard
Paired: yes
Trusted: yes
Blocked: no
LegacyPairing: yes
Connected: yes
UUIDs: 00001124-0000-1000-8000-00805f9b34fb Human Interface Device Service (HID)
UUIDs: 00001200-0000-1000-8000-00805f9b34fb PnP Information
Modalias: usb:v046DpB309d011B
Adapter: /org/bluez/hci0
Display More
So what can be the issue in LE? Bluez?