It sounds like a glitch. Just tested on my devices and it works fine with the iPhone's default ringtones. I don't have any custom ringtones that I can test with.
1. Make sure both your devices are updated to the latest iOS/iPadOS
2. Activate your Contacts in iCloud again. Both on your iPad and iPhone (Settings → Apple ID → iCloud)
3. Set the contact ringtone back to default on both your devices
4. Turn off both your devices. Wait a bit and turn them back on.
5. Make sure they are both connected to Wi-Fi
On either your iPhone or iPad, choose a different Default ringtone for the contact, and see if it syncs without going back to default again.