Okay. With benefit of your clarification, I now have a much better understanding of the situation...
On both your iPad and iPhone, disable iCloud Messages - and then disable Text Message Forwarding on your iPhone:
Settings > [Your Name / AppleID] > Messages - set to OFF
Settings > Messages > Text Message Forwarding - set to OFF
Next, perform a forced-restart of your iPad and iPhone:
Force restart iPad - Apple Support
Force restart iPhone - Apple Support
After restarting both devices, re-enable Text Forwarding on the iPhone:
Settings > Messages > Text Message Forwarding - set to ON - and again explicitly enable your iPad from the list of devices.
Finally, re-enable iCloud Messages on both the iPad and iPhone:
Settings > [Your Name / AppleID] > Messages - set to ON