Contacts missing after transfer to new iPhone

Contacts missing after transfer to new iPhone. But names appear only when searching to compose new messages?

Hi, I have transferred my data to my new iPhone but I have a lot of contacts that didn’t transfer over.

I’ve tried:

• Logging in and out of icloud on both devices
• turning contacts in iCloud settings on and off on both devices, with a wait in between to allow to sync
• Adding all groups/accounts that were present on my old phone (this re-added some, but not all contacts)

Interestingly, when I compose a new message and search for a name in the “to” field I can see the contact name and numbers. But the names and contacts are missing from my address book. Any ideas? I’m finding this very frustrating.