Without an associated iPhone, an iPad is fundamentally unable to send or receive SMS/MMS messages.
While iMessage can exchange messages with other Apple devices, if exchanging messages with Android or non-Apple devices, you’ll need to use Cellular SMS/MMS messaging.
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 enabled the built-in eSIM or added a DataSIM and Cellular plan to a WiFi+Cellular model of iPad, the number associated with the eSIM/SIM card is only used to identify your account for billing purposes. This number cannot be 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
