Wifi only iPad attempting to send SMS

Begin with a forced-restart of your iPad - as this will often clear an isolated software issue:

Force restart iPad (models with Face ID or with Touch ID in the top button)

If your iPad doesn’t have the Home button, do the following:

1. Press and quickly release the volume button nearest to the top button.
2. Press and quickly release the volume button farthest from the top button.
3. Press and hold the top button.
4. When the Apple logo appears, release the top button.

Force restart iPad (models with the Home button)

Press and hold the top button and the Home button at the same time. When the Apple logo appears, release both buttons.

If the problem persists after performing the restart, it may be necessary to reset your iPad settings. While this reset will not cause any loss of data, as a precaution, it is always wise to ensure that you have a current iCloud or iTunes backup before performing the reset:

How to back up your iPhone, iPad, and iPod touch - Apple Support

When you are happy to proceed, you can perform the reset from iPad settings:

Settings > General > Transfer or Reset iPad > Reset > Reset All Settings

If the problem still doesn’t clear, the next step is to reset the iPad to factory settings:

Restore your iPhone, iPad, or iPod to factory settings - Apple Support

Otherwise, you would be best advised to seek assistance directly from Apple Support. You can contact the Support Team using the Support link at top-right or bottom-left of this page. Alternatively and perhaps easier, you can initiate and manage your support cases using the excellent Apple Support App. If not already installed on your iPad, the App can be downloaded from the App Store:

https://apps.apple.com/app/apple-support/id1130498044

If exchanging messages with Android or non-Apple devices, you’ll need to use Cellular SMS/MMS messaging. If the iPad is paired with an iPhone, the iPad can relay SMS/MMS messages via the iPhone - but without an iPhone cannot exchange messages using Cellular. This obviously has implications for messaging between users that do not have an Apple device.

In more detail...

An iPad, whether a Cellular model or not, is not capable of directly accessing Cellular Voice or SMS/MMS Messaging features. An iPad with either WiFi or Cellular connectivity alone can only access IP-data services. If you have activated an iPad's eSIM (where available), or added a DataSIM and Cellular plan to a WiFi+Cellular model of iPad, the number associated with the SIM card is only used to identify your account for billing purposes. This number can not used for making calls or sending messages.

However, when paired with an iPhone, the capabilities of iPad significantly broaden to include access to Cellular Voice and Messaging services of the associated iPhone - relayed to the iPad over WiFi using Apple’s continuity features.

More information about Continuity and the relevant Cellular services can be found here:

Continuity

Use Continuity to connect your Mac, iPhone, iPad, iPod touch and Apple Watch – Apple Support

SMS/MMS Messaging

How to forward SMS/MMS text messages from your iPhone to your iPad, iPod touch or Mac - Apple Support

If you have an iPhone - and both iPad and iPhone are signed-in to iCloud with the same AppleID - to send SMS/MMS messages (green bubbles) from your iPad you must explicitly enable Text Message Forwarding for your iPad on your iPhone...

On your iPhone:

Settings > Messages > Text Message Forwarding - set to ON - and explicitly enable your iPad from the list of devices.

Also ensure that Messages in iCloud is enabled on both your iPhone and iPad:

Settings > [Your Name / AppleID] > Messages - set to ON

Armed with this knowledge, it follows that to disable access to SMS/MMS messaging from an iPad paired with an iPhone, you must disable Text Message Forwarding for the iPad from the paired iPhone.