How to sync old blocked texts to another Apple device?

Best way to get old blocked text messages to pop up when signing into another device with your Apple ID? I tried signing into my wife's iPad with my Apple ID and made sure all iCloud messaging was synced correctly. It weirdly combined texts/changed contacts photos and names differently than what is on my iPhone.

I want to sign in with my Apple ID onto a new device to retrieve old texts from a blocked number ( I have blocked voicemails on my iPhone, so I am sure that there are old texts too). Anyone done this before and can tell me exactly what to do? I tried following a TikTok example, then read something about it won't retrieve old blocked texts if you're on wifi (which I was at the time). Just trying to see if I can check and have them pop up on another device.

[Re-Titled By Moderator]