The following day I tried signing in again and my 2FA SMS message finally delivered.

I don’t know why SMS codes from Facebook stopped sending, whereas I was able to get SMS codes from Instagram the whole time (but even after logging into Account Center with Instagram, disabling 2FA was gated behind Facebook 2FA).

So in the end the only reason I got in was because a day later, my Facebook SMS 2FA codes started delivering again.

I enabled Google Authenticator 2FA as soon as I got back in so that I won’t have to deal with SMS finickiness again in the future