The blue recovery screen asks for your 48-digit recovery key that you've never seen before. The hard drive that held all of your files is now negotiating. BitLocker recovery is two types of disciplines: finding those keys that users did not know they had, and recovering the failing hard drive through its own encryption. The bench does both of them, with the true limits clearly defined from the beginning.
BitLocker seldom enables without saving some form of the recovery key somewhere, so finding it is the issue. The checklist below will help you solve most lockouts: your Microsoft account (account.microsoft.com → Devices → recovery keys: this is the modern Windows default, and the solution for most home users who 'never turned BitLocker on', as it was enabled when they got their laptop); work or school accounts, where IT's Azure AD or Active Directory stores keys; the printout or file made at setup (a search for "BitLocker recovery key" in emails and cloud storage finds old ones every week); and the USB stick older setups used. Every candidate identity should be brought to the diagnostic. Matching key IDs to the drive is part of the service.
In the worst-case scenario, you're dealing with a dying disk and a BitLocker-locked one at that: bad sectors in your encrypted data area, or your laptop went down and booted into recovery mode because the drive beneath it is sick. There's order to things when dealing with this type of problem: first, we stabilise the original failing drive and capture an image of it, with encryption still active, to prevent the failing hardware from burning out while attempting unlocks; second, we decrypt the healthy image using your key. TPM issues (replacing the board or changing the firmware, which will kill auto-unlocking) are treated similarly. Lastly, let there be no misunderstanding about this: if your key cannot be retrieved from any source, then you won't have access to your decrypted files, because the encryption was designed to work this way mathematically; therefore if someone is claiming they can give you access when you've lost your key, they are selling something.
Almost certainly in a Microsoft account: on modern laptops, device encryption is enabled silently during the initial boot-up; the key to access this device will be stored remotely by Microsoft as soon as you log into the machine. In order to check all devices which have been associated with your Microsoft account, simply visit account.microsoft.com under Devices, and search through all of the accounts you've ever used on that machine (including some you may have forgotten about). This should resolve the majority of "I didn't turn it on" lockout scenarios.
Always the failure: when attempting to unlock a locked-plus-failing drive, each boot attempt costs some of what remains of the drive's life. In addition, each attempt to unlock the drive means very expensive read operations. The bench images the drive while it is still encrypted, gently, then uses your key to decrypt a stable image of the drive. Locked-plus-failing is routine here, provided the key exists.
No, and to be honest no one credible can. If BitLocker is implemented correctly, then without your key, password or TPM cooperation, it is designed to be unbreakable. That is still true today. What we can do is run through all possible escrow locations (which people seem to find every week) and recover your drive, so the data is ready as soon as an appropriate key comes forward.