When you login to the website or you do some transactions with their card (online or shops) they might send you SMS. But not if you have the app registered as 2FA device.
And VPN: yes. Has nothing to do with the question at all
Install the wise app in a phone. Then you’ll not get SMS.
As for banks: no chance if they don’t already have some sort of security app. But you might try their app too.
And VPN: how does that help????
You receive SMS exactly the same with or without VPN which is for data over internet and not for GSM protocol (SMS and phone calls).
But from your questions I guess that you might also profit from another phone setting:
WiFi calling
If it’s on (might take a day), then whenever your in WiFi you phone will replace the name of your provider (like AT&T) by something like “WiFi calling”). Your phone is then virtually relocated to your home country. So calls to home are cheap or free and calling Thailand is overseas.