I read the federal government’s Zero-Trust Memo so you don’t have to

> “discontinue support for protocols that register phone numbers for SMS or voice calls, supply one-time codes, or receive push notifications."

... necessarily means TOTP.

Could be argued "supply" means code-over-the-wire, so all 3 being things with a threat of MITM or interception: SMS, calls, "supply" of codes, or push. Taken that way, all three fail the "something I have" check. So arguably one could take "supply one-time codes" to rule out both what HSBC does, but also what Apple does pushing a one-time code displayed together with a map to a different device (but sometimes the same device).

I'd argue TOTP is more akin to an open soft hardware token, as after initial delivery it works entirely offline, and passes the "something I have" check.

TOTP apps are certainly better than getting codes via SMS, but they're still susceptible to phishing. The normal attack there is that the attacker (who has already figured out your password) signs into your bank account, gets the MFA prompt, and then sends an SMS to the victim, saying something like "Hello, this is a security check from Your Super Secure Bank. Please respond with the current code from your Authenticator app." Then they get the code and enter it on their side, and are logged into your bank account. Sure, many people will not fall for this, but some people will, and that minority still makes this attack worthwhile.

A hardware security token isn't vulnerable to this sort of attack.