Sending and receiving Messages on my iPad

Is this difficulty isolated to SMS/MMS text messages (green bubbles), or all messages including iMessage (blue bubbles)?

Your iPad can only send/receive SMS/MMS text messages if they are relayed via an iPhone. SMS/MMS messaging requires access to Cellular Carrier services not natively supported by iPad.

If you don’t have an iPhone, you can only send iMessages between Apple devices. As the iPad does not have access Cellular text services, without an iPhone, it cannot alone send SMS/MMS messages.

If you do have an iPhone, in Settings of the iPhone:

Settings > Messages > Text Message Forwarding - set to ON

Are you signed in to your Apple ID and have you enabled iCloud for messages? If you did then maybe try to sign out and sign in again. Good luck