How can I add Emergency Contacts on locked iPad 18.2.1 with screen time restrictions?

System features - and in some cases Apps - differ between iOS (for iPhone) and iPadOS (for iPad).

The Apple Health App and presentation of Emergency Contact information is just one example of differing functionality between these two different (but related) platforms.

While you cannot use the Health App to display Emergency Contact Information on the iPad Lock Screen, there is a potential workaround using the Lock Screen WallPaper image...

Create a Lock Screen Image - then edit the image to include the text that you wish to display. When you have the image ready, you can set this image as the Lock Screen Wallpaper - noting that the Lock Screen and Home Screen Wallpaper images can be set individually, or as a pair.

Change the wallpaper on iPad - Apple Support

the Emergency Contacts in the health app on iphones is who to contact if the iphone detect a car crash or if the apple watch detect a fall, since the ipads do not have the sensors to detect a crash or the ability to sync with an apple watch, so maybe whatever expectation of what being the kids emergency contact is something else then that, maybe elaborate ?