de0u it will plausibly also leak its HOTP/TOTP secrets.
Just to add a little to this so everyone properly understands.... HOTP/TOTP use SHARED SECRET encryption. That means that the magic bits are known to BOTH SIDES of an encrypted transaction, so in the event of a server breach, it is conceivable for a bad actor to get themselves a copy of EVERY USER'S secrets, which can be used to generate those 6 digit codes.
It would be so much better to send a public key signature of a timestamp to a server to authenticate since the private key (not available to server) is needed to generate the signature, which can be validated with just the matching PUBLIC key. Bad actors can copy all the public keys they want and that's perfectly OK since the public key CANNOT be used to generate a signature, only verify it. The problem with using a public key signature of course, is that you can't truncate it to 6 digits and retain the ability to verify identity. Well with authenticator software, its easy enough to copypaste a much longer signature.