The error 0x2 (WIN32: 2 ERROR_FILE_NOT_FOUND) combined with SCardGetCardTypeProviderName failing is definitive: the Calais Database (the Smart Card registry hive) does not have an entry for the ATR 3b 7f 96 00 00 00 6a 43 52 59 50 03 04 11 43 01 00 03 90 00. Essentially, the electrical layer (the reader) sees the card, but the logical layer (Windows Resource Manager) has no idea which DLL to load for that specific byte sequence, so it fails before it can even attempt to load a driver. This often happens after a major Windows feature update (like 25H2), as the update process can scrub the registry of "third-party" smart card entries that aren't backed by an active, digitally signed PnP driver package it recognizes as valid for the new kernel.
You need to verify the registry state immediately. Open Registry Editor (regedit.exe) and navigate to HKEY_LOCAL_MACHINE\SOFTWARE\Microsoft\Cryptography\Calais\SmartCards. You are looking for a subkey that matches the ATR (often stored as a binary value or a subkey name derived from the ATR mask). Since certutil failed to find it, it is almost certainly missing. In a functional environment, you should see a key there containing values like 80000001 (pointing to your minidriver DLL name) and Crypto Provider (usually "Microsoft Base Smart Card Crypto Provider").
To resolve this, you must re-register the card's ATR in the Calais database. Since you are in a driver development environment, locate the .inf file associated with your minidriver project. Right-click that .inf file and select Install. This performs the [Install.AddReg] directives that write the ATR and DLL mapping into the registry. If you cannot reinstall via INF, you can force the mapping using certutil in administrative mode: certutil -addcard -c "Your Card Name" "YourMinidriver.dll". You will be prompted to enter the ATR; copy the exact hex string from your output (3b 7f 96...) and paste it there.
Once the registry key is restored, verify that the minidriver DLL (e.g., yourminidriver.dll) physically exists in %SystemRoot%\System32. Note that if your HLK test suite is running as a 32-bit process on this 64-bit OS, you must also ensure the DLL is in %SystemRoot%\SysWOW64 and the registry entry exists in HKEY_LOCAL_MACHINE\SOFTWARE\WOW6432Node\Microsoft\Cryptography\Calais\SmartCards. Without this dual registration, the 64-bit OS sees the card, but the 32-bit cmck.exe test harness will still fail with "File Not Found."