Earlier quoted context omitted.
TOTP or SMS, it's just another text password you're entering in that's fully phishable. TOTP just "feels" more secure.
No, TOTP is far more secure because it has no dependence on a third-party who can mess up in many ways (Denial of service like in this case by being unavailable, Impersonation by allowing SIM swaps or intercepting messages directly). You fully control how to store the TOTP seed and how you compute the value, so it is far more secure. Yes, it can be phished if you fall for that, but it removes several attack vectors.
Sorta. The seed still needs to be issued to you in some way.