Hello
It sounds like you're experiencing a frustrating issue with Windows Hello and Bluetooth second factor authentication after rebooting your laptops. Here are some steps and considerations that might help resolve this issue:
Bluetooth Adapter Check: Ensure that your Bluetooth adapter is properly connected and recognized by your system. You can check this by going to Start > Settings > Bluetooth & devices and making sure Bluetooth is turned on.
Passkey Setup: Make sure that the passkey setup on your mobile device is correctly configured. This can be crucial for the Bluetooth pairing process.
Windows Hello for Business: If you are using Windows Hello for Business, ensure that the PIN and biometric settings are correctly configured. This can help streamline the login process and reduce delays.
Identity Access Management Support: If you encounter errors during the authentication process, try closing all browser sessions, restarting your browser, and attempting the registration again. Using InPrivate browsing might also help.
Unlock Policy Definition: Review your unlock policy to ensure that the correct second unlock factors are being used. For example, using a combination of PIN and Bluetooth phone or network location might help improve the authentication process.