This is one of those jobs I have done several times but couldn't remember why it didn't work the next time.

You add a client certificate to your personal store under Current User, it is in-date, it chains OK but when using Windows Credential Manager to add a connection, it doesn't offer you this certificate to choose,.

As pointed out here, you have to edit the properties of the certificate and untick "Smart Card Logon" and "Any Purpose" otherwise Windows will ask for a Smart Card to access the client cert!