How do I get my iPhone 11 and iPad to sync iMessages?

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

More information:

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

Fault finding if needed:

If you can't send or receive messages on your iPhone, iPad, or iPod touch - Apple Support

Messages are synched through iCloud. Make sure that both devices synch to iCloud. The procedure is the same for both devices and you need to apply it to both devices:

1. Open Settings
2. Tap your name
3. Tap iCloud
4. Make sure that Messages is turned on