Backup the system's "Personal Dictionary" on Android 7 and import on different phone?
It is quite odd that it isn't syncing across devices. I know that recommending an application may not always be the best solution but I did just try Personal Dictionary Backup on my Xperia XZ running 7.0 and it was able to backup and restore my personal dictionary. 

Do keep in mind that it backs up to a .dat file on your internal storage. The folders name that it backs up to is "UserDictionaries". This means that you would have to digitally transfer the .dat file in that folder to your new device in a folder with the same name as well as installing the app on your new device.