My Apple devices all receive verification codes and texts fine, but my new iPad does not. Why?

A bit of explanation first :)

When my Old iPhone got slow and I needed more memory I upgraded it to a new one. I keep Old iPhone just running on wi-fi, just handy to have a spare one around. The two are more or less clones of each other, and they both receive texts and MMS identically.

When the same happened with my Old iPad, I did the same. Upgraded to New iPad and kept Old iPad for around the house on wi-fi.

Old iPhone, New iPhone, and Old iPad continue to receive texts and MMS, all identically

But New iPad specifically does not pick up verification codes, banking messages, etc. Why could this be, when all the other devices do? It can't be a fault in the apps or the numbers the messages come from, because they are picked up fine by the other three devices.

Other texts (from friends etc) arrive on New iPad no problem, it's just authentications, verifications, codes, etc that it won't pick up.

The Blocked Sender list is the same on all devices, so can't be the issue

All devices are running on the latest iOS.

I have tried the following on the New iPad:

• Toggling "Settings, Messages, Filter Unknown Sender" on and off - it's obviously set to OFF
• Toggling "Airplane Mode" on and off (sometimes a fix for all sorts of things)
• Rebooting (home button + power button)

Any other ideas, anyone?

Thanks!