I would suggest following Apple's guide on recovering an Apple-ID:
In particular you want to visit this web site to start the process:
If these are the steps you've already taken, and you still cannot gain access even after waiting the given period of time - I would call Apple Support to ask ...
The most logical answer to this is that it is not sending international SMS messages after activation is done, so it must be something else your carrier is charging you for.
I would contact your carrier to get an explanation of the costs.
As far as I understand, many carriers have business relationsships with Apple and ensure that you are not charged for ...
As of June 17, 2020 you can not turn off two-factor authentication and you can not use some features without enabling it. It was optional, highly encouraged and opt-in on iOS 12 and iOS 13.
Can I turn off two-factor authentication after I’ve turned it on?
If you already use two-factor authentication, you can no ...