If you are willing to "loosen" your requirements slightly, VOIP.ms (https://voip.ms/) VOIP phone numbers support SMS send/receive (including a web interface in your account to do send/receive) and using one to send/receive SMS codes would be relatively inexpensive (if you pick their "pay for usage" version).

This page shows their pricing in various countries (https://voip.ms/business/pricing#improved_communications_con...). For the US the "pay for usage" variant costs $0.85/month for the number itself plus $0.0075 per SMS message (for basic SMS messages).

You can configure the number to return the "out of service tones" if you don't want to use it for calling, but as you do mention "traveling abroad" then with a VOIP number you could send/receive calls from anywhere you had a working internet connection to one of their servers. VOIP.ms works perfectly with Linphone (both Linux desktop and Android app from F-Droid: https://f-droid.org/en/packages/org.linphone/) for calling (at least for phone usage, I've not attempted using Linphone's fancy IM or video calling).

As to whether VOIP.ms is available "in your country" -- I'll have to let you investigate that for yourself.