There appears to a mix of customers here with card accounts as well as some who also have deposit accounts.
There is definitely not an easy solution for international sms. I have found wifi calling if you buy a plan from the US does work for sms texting over wifi. Once you get app access, the agent can also send a message to the app if needed to authenticate when on the phone.
I don't know if Travel Notices (which Capital One no longer supports) help because if your card is stolen, they would likely try to use the card in the same country. They all have gone to some AI type of fraud engine which even if you clear the first denial, it can happen again.
But I do like the real time transaction notification from the app. I don't get the same type of function for all the other banks, which some have.