I will be traveling overseas in a few weeks, and I am trying to figure out if installing an eSim on my phone will let me still check my US phone and text messages while I am out of the country. I believe I understand the eSim will enable me to use my phone and apps in the other country via wifi (through whatever local number I get through the eSim), but will I still be able to use my usual US phone number via wifi in the other country as well?
eSIM and physical SIM should behave the same way.
I see that you have added iPhone 12, in this case you can use both one physical sim and one eSIM.
If you have physical SIM card with Visible, you can activate eSIM with the local provider (temporary sim at foreign country) or vice versa.
Visible will work if you had enabled "Wifi calling" while you are in US connected to Visible network.