Why doesn't my password manager support the passkey?

Only password managers that are FIOD2-compliant are supported

Only password managers that are FIOD2-compliant are supported. Many password managers can store passkeys, but are not compliant themselves and are therefore not authorised by Swisscom Trust Services for security and regulatory reasons. 

Information on passkeys that are compliant can be found under "Supported FIDO2-compliant passkeys".