Hi, @Johannes
On most modern PCs, the TPM chip that stores your Windows Hello PIN and passkeys is built into the CPU. When you swapped the CPU, that storage was wiped. Windows is still pointing to the old data, so it falls back to asking for a "Security key" that doesn't exist. Your old passkeys can't be moved to the new CPU, but you can clear out what's left of them.
Here are some suggestions you can try:
Make sure the TPM is turned on. Restart into the BIOS and check that AMD fTPM or Intel PTT is enabled. A CPU swap can switch it off. Back in Windows, press Win + R, type tpm.msc, and check that it says "The TPM is ready for use."
Clear the old PIN data. Before you start, make sure you know your Microsoft account password, because you'll need it to sign in afterward. Open Command Prompt as administrator and run: icacls C:\Windows\ServiceProfiles\LocalService\AppData\Local\Microsoft\Ngc /T /Q /C /RESET Then go to that folder, delete everything inside Ngc, and restart. Next, go to Settings > Accounts > Sign-in options and set up a new PIN. This removes the leftover passkeys that are tied to the old CPU.
If it still asks for a security key, go to Windows Security > Device security > Security processor details > Security processor troubleshooting > Clear TPM. If BitLocker or Device Encryption is on, save your recovery key from aka.ms/myrecoverykey first.
After that, sign in to each website with your password and create a new passkey there.