iPhone 13 mini Bluetooth cannot pair with other devices

I recently purchased a refurbished iPhone 13 mini. Everything works fine. The WiFi works regularly. The USB works fine.

But I can't pair it to anything via Bluetooth.

1. Bluetooth can be switched on, and Facetime can see it among the devices to be used as a camera.
2. The iPhone (iOS 18) can see the Mac mini M4 Pro (macOS 15) in the Settings > Bluetooth page.
3. When I touch the Mac mini name in the Bluetooth page in the iPhone, I get a messages saying that I can't connect.
4. The iPhone (iOS 18) can see the iPad mini 4 (iPadOS 15) in the Settings > Bluetooth page. The iPad can see the iPhone.
5. When I touch the name of the other devices, in the iPhone or the iPad, I get the message saying that I can't connect. The iPad can connect to the Mac and other devices.

I've tried to solve the issue on the iPhone:

• Turned Bluetooth on/off.
• Rebooted the iPhone.
• Started by keeping the Power button for 8 seconds (the iPhone rebooted during the power-on cycle).
• Initialized the Network from Setting > Transfer > Reset.

None of the above worked. Apparently, the hardware is working, since the iPhone can see and be seen by other devices. So, what's going wrong?