How to restore WhatsApp data from SD card or internal memory and not from Google Drive?
I had problems with this too, and today finally it worked.  Unfortunately I'm not sure which of the following additional steps did the trick, but maybe it helps others:


I copied the entire WhatsApp folder over from the old phone to the new one (zipped it using Total Commander, copied it to a PC via USB, copied it to the new phone also via USB, unzipped it also using Total Commander).
After installing WhatsApp, I gave the app all possible permissions before running it: under Settings/Apps, select WhatsApp, tap Permissions, and then select all permissions listed under "denied" and tap "allow" (you can revoke the permissions again after the backup is succesfully restored).


After doing this, running WhatsApp and confirming my phone number, I was finally prompted to restore the local backup. Before that, WhatsApp asked me for some permissions and then asked me to select a Google Drive backup (which I hadn't done), when I selected "skip" at this step it apparently also skipped the local backup.