Black screen with cursor after login on Windows 11 - Startup Repair, SFC, and System Restore didn't fix it

Hello everyone,
I have an HP laptop running Windows 11 (exact model unknown).
My laptop boots normally to the login screen. After I enter the correct password, the screen turns black with only the mouse cursor visible. I cannot reach the desktop.
This started immediately after I deleted the C:\$Windows.~BT folder while trying to free disk space after a failed Windows Update.
Things I have already tried:
Startup Repair (did not fix it)
System Restore (failed)
Safe Mode (did not help)
sfc /scannow (no integrity violations)
BitLocker unlocked successfully
bcdedit shows osdevice partition=C:
Winlogon Shell = explorer.exe
Winlogon Userinit = C:\Windows\System32\userinit.exe,
I do not want to reset or reinstall Windows because this is my brother's laptop and I need to preserve all data.
Is there any way to repair this black screen issue without resetting Windows?

HKEY_LOCAL_MACHINE\SOFTWARE\Microsoft\Windows NT\CurrentVersion\WinLogon



check StringValue "Shell" and make sure its value is set to "Explorer.exe"

I'm guessing you didn't make a system image backup before the update?

Try a Repair install Settings > System > Recovery > Fix problems with Windows Update