Hi Jeanne,
This appears to be an issue with the Microsoft account verification page rather than BitLocker itself. Since you can sign in and see the device, but the BitLocker Recovery Keys page gets stuck in a sign-in loop, try accessing it from a different browser, a different device, or a different network (for example, a mobile phone using cellular data instead of Wi‑Fi).
Also verify that third-party cookie blocking, privacy extensions, VPN software, or network filtering are disabled, as Microsoft's account and recovery key pages rely on multiple authentication redirects. If possible, sign out of all Microsoft accounts, close the browser completely, then sign back in using only the account associated with the locked device.
If the recovery key page continues to loop across multiple browsers and devices, contact Microsoft Account Support, as this is likely an account authentication issue on the BitLocker portal rather than a problem with the encrypted device itself. Without access to the recovery key, there is no supported method to unlock a BitLocker-protected drive.
Harry.