Error recovering MacBook login password: “There was an error communicating with iCloud”

I forgot my Apple MacBook Pro M2 password yesterday (running on MacOS Sonama) and after multiple tries, I tried to recover using recovery options provided by apple. After following all the steps loging in using my Apple ID.

In the reset password process, after I logged in using my Apple ID, it suddenly shows error “There was an error communicating with iCloud. It happens right after the step where it tries to load FileVault recovery key.

I do have my FileVault recovery key and have all other passwords.

After contacting with Apple support and have a long conversation and they re-tried all the steps, they simply said: “well, you can only remove everything in your mac, we can’t help you more”

I even tried doing it using the terminal, and I can see a bunch of error printing in the terminal. Here I attached screenshot:

Error above clearly indicates:

NSSoftLinking - The Shortcut framework’s library couldn’t be loaded from (null).

The function ‘SCTInitShortcut’ can’t be found in the Shortcut framework.

AOSKit: ERROR: CFBundleCreate failed (AppleAccount)

ERROR: Failed to load AppleAccount

and continues:

Missing ep for BTMM

Any idea? It seems I can’t try more passwords as when I try to enter new passwords it says “Account is locked”.

I can’t simply lose my data, it’s my PhD work/codes, and I don’t have backup. Can I do anything with the FileVault recovery key that I have? I don’t mind reinstall everything, but even reinstalling asks for password, which now seems locked.