I tested it (restoring from local backup on a new phone) and it does work but it's really not straight-forward compared to e.g. restoring a Signal backup.
I mostly followed this comment at it worked. Here's my slightly amended guide:
1) Install WA on the new phone. Just open it once but do not do absolutely anything. Then close the app, force stop it, clear the cache and storage, and don't allow it to run in background.
2) from the old phone (or from a manual backup of the folder structure) copy the entire com.whatsapp
folder from /storage/emulated/0/Android/media/
including hidden files onto the same location of the new phone. Check that you end up having a folder called /storage/emulated/0/Android/media/com.whatsapp/Whatsapp/Backup
and a folder called /storage/emulated/0/Android/media/com.whatsapp/Whatsapp/Databases
both containing several files ending in .crypt14
.
3) Open WA, choose language, and enter in SMS verification code to activate and enter your 2-step verification PIN if you have enabled this feature.
4) Now immediately turn airplane mode on to block WA from contacting Google's services.
5) Grant all permission requests that come up, especially contacts and storage access.
6) Let WA try to access Google Drive. It should say that it cannot connect to GDrive. A prompt should pop up. Skip, and you should be prompted to restore from a local backup.
7) The first time the restore from local backup will fail as it needs Internet. So, disable airplane mode again and let WA retry. Now it should work.