How can I add my iPad back to iCloud without a PC

Once removed it cannot be added back, except by signing back into your Apple ID on the iPad itself.

You will need a computer to restore it though, if its disabled or in accessible. Borrow one from a friend or relative or go to an Apple Store and ask to use one in the store.

For devices with iPadOS 15.2 or later* you may be able to use the method in this support article: If you forgot your iPhone passcode or your iPhone is disabled - Apple Support This does not require a computer. You say yours is running iOS 18 so you might be able to regain access without a computer.