I know because the messages on my NEW phone that I am trying to set up state "We sent this to (your old phone -- identified by type of phone, which is different from the model I am setting up).
I think there's some confusion about messaging. If Google knows the model/name, then it's likely not SMS being sent, but rather one of the "review this login" system pop-ups.
See if you can revert to SMS verification through some option at login. I can't verify it now, but the choice could be accessible though something non-obvious like "I'm having problems verifying". Make sure it's trying to use a text message instead of some other method... and let's hope you have it configured.
This is because Google has a disaster of a 2FA process where even if you have 2FA disabled, they will "send a prompt to the Google app on %s device" to verify it's you. What happens if that device doesn't have the Google app installed? You're screwed. The only fix for this is to, paradoxically, ENABLE 2FA, which then you can force to go ovet text.
