I have managed to ditch WhatsApp (thankfully) and it has been years since I last had to migrate to a new device. The process was quite simple, at least as far as I can remember.
First, navigate to the backup menu (in WhatsApp) where you are supposed to choose a Google account and backup frequency. I think there should be a button named "backup now" or something. This will create a local backup located at Android/data_or_media/whatever_whatsapps_app_id_is. Browse the directory and you should see your backup in a nested folder.
Then, migrate this folder to the new device and put it in the same location before installing WhatsApp. After you install and open WhatsApp, it should prompt you to import your old messages from the backup.