Took physical SIM card out of old iPhone11, put it in new iPhone14. Lost access to mobile data from SIM card on both devices. Could not log into Apple ID on old or new device, required sms for 2 fact. auth. Apple ID regained through 7 day process

That normally means there's an issue with the SIM card out the phone trying to read the SIM card so cannot correct use the configuration info on it to connect to your service provider. It is strange that it works normally in a different phone however.

Have you contacted your service provider? They may need to give you a new SIM card.

It's also possible, if you started the eSim migration, the phone knows this, and won't use the SIM card data anymore, since it's waiting for the SIM card to be activated.

I think you need to contact your service provider for help at this point.

It should work in the iPhone. What happens when you insert it into either iPhone exactly?

When you insert it into either iPhone, do you not see your the signal strength and connection type at the top?

Do you just see No Service?

What exactly happens?

Have you contacted your carrier to find out why it didn't work?