Contacts on iCloud

See the article Remove apps from iPad - Apple Support

Note: When you delete a built-in app from your Home Screen, you also delete any related user data and configuration files. Removing built-in apps from your Home Screen can affect other system functionality. See the Apple Support article Delete built-in Apple apps on your iOS 12, iOS 13, or iPadOS device or Apple Watch.

Restore a built-in app that you deleted

1. On your iOS or iPadOS device, go to the App Store.
2. Search for the app. Make sure that you use the exact name of the app. Find the correct name of built-in apps.
3. Tap  to restore the app.
4. Wait for the app to restore, then open it from your Home screen.

If you have an Apple Watch, restoring an app to your iPhone also restores that app to your Apple Watch.

What happens when you delete built-in apps from your device

Deleting built-in apps from your device can affect other system functionalities. Here are some examples:

• If you have an Apple Watch paired with your iPhone, deleting an app from your iPhone also deletes that app from your Apple Watch Home screen.
• If you delete the Podcasts app from your device, Podcasts won’t be available with CarPlay.
• If you delete the Stocks or Weather app from your device, stocks and weather won’t be available elsewhere. For example, you won’t see stocks and weather information in Notification Center on your iPhone or as Complications or Glances on your Apple Watch.
• If you delete the Calculator app, the calculator won’t appear in Control Center.

To restore an affected functionality, you can add built-in apps back to your device.

When I go to http://icloud.com/contacts running Safari on an iPad Mini 4 v15.7.2 and iPad Pro v16.2 I get this screen:

Turn on contacts box from iPad so that they sync with iCloud Set up iCloud for Contacts on all your devices - Apple Support

See an additional article Use other contact accounts on iPad - Apple Support

Same problem. No Contacts icon when running iCloud.com on iPad Pro v16.2. Contacts seem okay on iPhone and iPad.