I would like to point out that, if most sites used two-factor authentication, this leak would be at most a minor inconvenience. Maybe we should push for that more. Just days ago I talked to Namecheap about its horrible SMS-only 2FA and asked them to implement something actually secure, maybe contact your favorite site if they don't have 2FA yet.
If you setup TOTP (Authenticator) while this bug was out in the wild your shared secret key could have leaked. SMS would actually be safer than TOTP in this scenario.
TOTP works by having (as you said) a shared secret key, and both sides calculate an HMAC of the secret along with the timestamp, and then just modulo the resulting HMAC by 10^6 (usually, for TOTPs with six digits).
Your google authenticator (or whatever) app does this HMAC on the shared secret + time, you type in six digits, and the other side does the same HMAC and verifies that they're the same. If they're UX-conscious, they might decide to HMAC the previous and next 30 second periods as well and compare those too, to account for small amounts of time skew.