In-depth Troubleshooting of HandOff/Universal Control issue on Macbook

Trouble Description: Macbook HandOff doesn't connect to iPad/iPhone while AirDrop works fine. In the system Setting of the Macbook, there is no + button shown at all. Plus the Sidecar function can not connect to iPad as well. (No HandOff function Problem between iPad and iPhone)

Devices Information: Macbook 2017 with macOS Ventura 13.6.4 (22G513)

iPad Pro 12.9 4th wich iPadOS 17.3

(both meet the compatibility requirements and signed in to iCloud with the same Apple ID.)

Troubleshoot steps already taken:

1. Turn On/Off Setting> General>AirDrop&HandOff>Cursor and Keyboard on iPad and Preferrences>Display>Advanced Button “Allow your pointer and keyboard to move between any nearby Mac or iPad.” on Macbook.
2. Turn On/Off Bluetooth and AirDrop on Macbook and iPad.
3. Sign In/Out Apple ID on both devices.
4. Restart both devices.
5. Uncheck "Allow Handoff between this Mac and your iCloud devices." and restart the Macbook. Then re-enable HandOff by checking the same option.
6. They are placed right near each other.
7. No cellular connection was shared.
8. Run through a hardware check on the Macbook by pressing D on the keyboard.
9. Reset Bluetooth on the Macbook with code

sudo pkill bluetoothd

I have gone through every possible troubleshooting step I can find and the issue still isn't solved.

Any help regarding this issue would be appreciated.

Thanks~