Sometimes when you're switching between SIMs on an iPhone or iPad, your iMessage settings need to be reset in order to work properly.
- Tap "Settings"
- Tap "Messages"
- Toggle "iMessage" to OFF and wait a second
- Toggle "iMessage" back to ON
- You'll see it says "Waiting for activation"
- Tap "Send & Receive"
- Make sure your Apple ID email address is checked off
Selecting your email address will allow you to continue to send and receive iMessages using your brand-new eSIM data connection, without relying only on your phone number.