I bought my Macbook Pro 15" 2016 and restored the Time Machine back-up of the MacBook 12" 2016 everything seems messed up iCloud notes are not syncing and something removed notes/folders reappear and every time I log out of iCloud with the MacBook Pro it forces me to change my iCloud password when I log back in.

Now my iPhone and icloud.com are not syncing anymore either most of the time, sometimes it still works.

Some screenshots, although this has improved. I think the Rocketchat-thing might be Rocketchat's fault, but not sure:





Everything worked perfectly on the MacBook 12" 2016 and the iPhone though. I was very happy, except it wasn't well suited for BYOB and high cpu requirements.

PS: I have no recovery partition either. Not sure that is important, but means I can't use "Find my Mac". The MacBook was sold to me as refurbished at a very reliable retailer. I don't think it's a hardware issue, I did the NVM and SMC reset. Even created a new "test" new administrator user account, that made notes sync well, until my iPhone got involved.
Since you have a backup, why not boot to Internet Recovery and reinstall a brand new OS and test things. If there is something wrong with the hardware, you surely can get a feeling of that with a clean install.

The reliable retailer would likely help you if you can show that a clean install causes issues. If the system is stable, you could run Migration Assistant to move things over more slowly than just restoring all the programs and user data. First do one, then the other to see if there was a problem with the migration or just a bad migration.