Hi,
1.Please confirm what kind of private resolvable address you are referring to? Is it Mac address?
"To ensure that a unique container ID is generated for every device, developers of Bluetooth devices must configure each device with a unique MAC address."
https://learn.microsoft.com/en-us/windows-hardware/drivers/install/container-ids-for-bluetooth-devices
2.What is the exact error message you failed to reconnect and pair the Bluetooth device? Please follow general steps provided in below article.
Fix Bluetooth problems in Windows 10
https://support.microsoft.com/en-us/windows/fix-bluetooth-problems-in-windows-10-723e092f-03fa-858b-5c80-131ec3fba75c
3.Kindly check the Recommended experiences for Bluetooth Swift Pair.
https://learn.microsoft.com/en-us/windows-hardware/design/component-guidelines/bluetooth-swift-pair#recommended-experiences
Hope this helps and please help to accept as Answer if the response is useful.
Thanks,
Jenny