I know T-mobile and Verizon have handy apps you can use to receive regular SMS messages over your data connection. I assume AT&T does too. Verizon's is called Message+ and T-mobile's is Digits. I have used Message+ to send/receive SMS from my Verizon number while using a foreign SIM.

With the advent of eSIMs, you can (at least on iPhone) set the phone to use the Verizon SIM through the roaming eSIM - to Verizon it appears you're using wifi calling.